Solve tanalpha=sigma^2/26

$$\tan \alpha = \frac { \sigma ^ { 2 } } { 26 }$$

Solve for σ (complex solution)

$$\sigma =-\sqrt{26}i\sqrt{-\tan(\alpha )}$$

$$\sigma =\sqrt{26}i\sqrt{-\tan(\alpha )}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}+\frac{\pi }{2}$$

Solve for α

$$\alpha =\pi +2n_{3}\pi +arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})\text{, }n_{3}\in \mathrm{Z}\text{, }\exists n_{42}\in \mathrm{Z}\text{ : }\left(n_{3}>\left(-\frac{1}{2}\right)\left(\frac{1}{2}\pi +arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})+\left(-1\right)\pi n_{42}\right)\pi ^{-1}\text{ and }n_{3}<\left(-\frac{1}{2}\right)\left(\left(-\frac{1}{2}\right)\pi +arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})+\left(-1\right)\pi n_{42}\right)\pi ^{-1}\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\pi +2n_{3}\pi +arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})=\frac{1}{2}\pi +\pi n_{1}$$

$$\alpha =arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})+2\pi n_{22}\text{, }n_{22}\in \mathrm{Z}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})+2\pi n_{22}=\frac{1}{2}\pi +\pi n_{1}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }arcSin(\sigma ^{2}\left(\sigma ^{4}+676\right)^{-\frac{1}{2}})+2\pi n_{22}=\frac{1}{2}\pi +\pi n_{1}$$

Solve for σ

$$\sigma =\sqrt{26\tan(\alpha )}$$

$$\sigma =-\sqrt{26\tan(\alpha )}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(\alpha \geq \pi n_{1}\text{ and }\alpha <\pi n_{1}+\frac{\pi }{2}\right)$$