Solve for a
a=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\pi +arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\frac{5}{18}\times 6^{\frac{1}{2}})+2n_{1}\pi \right)
a=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(2\pi n_{5}\right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\pi +arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\frac{5}{18}\times 6^{\frac{1}{2}})+2n_{1}\pi \right)
a=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\pi +arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\frac{5}{18}\times 6^{\frac{1}{2}})+2n_{1}\pi \right)
a=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\pi +arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\frac{5}{18}\times 6^{\frac{1}{2}})+2n_{1}\pi \right)
a=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(-1\right)\times \left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\left(-\frac{5}{18}\right)\times 6^{\frac{1}{2}})+2n_{2}\pi \right)
a=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(2\pi n_{5}\right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(2\pi n_{5}\right)^{\frac{1}{2}}=\left(-1\right)arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\left(-\frac{5}{18}\right)\times 6^{\frac{1}{2}})+2n_{2}\pi \right)
a=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(-\frac{1}{2}\right)\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\left(-\frac{5}{18}\right)\times 6^{\frac{1}{2}})+2n_{2}\pi \right)
a=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}\text{, }not(n_{5}<0)\text{ and }\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\frac{1}{2}\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-\frac{1}{2}\right)\times 2^{\frac{1}{2}}\left(1+4n_{5}\right)^{\frac{1}{2}}\pi ^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\text{ or }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)\times 2^{\frac{1}{2}}\pi ^{\frac{1}{2}}n_{5}^{\frac{1}{2}}\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\frac{1}{2}\times \left(2\left(1+4n_{5}\right)\pi \right)^{\frac{1}{2}}=\left(-1\right)arcSin(\frac{1}{9}\times 3^{\frac{1}{2}}+\left(-\frac{5}{18}\right)\times 6^{\frac{1}{2}})+2n_{2}\pi \right)
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