Atrisiniet sin(4x)/1+cos(2x)=frac{sqrt{3}}{3}

$$\frac{ \sin ( 4x ) }{ 1+ \cos ( 2x ) } = \frac{ \sqrt{ 3 } }{ 3 }$$

Atrast x

$$x=\left(-1\right)arcSin(\frac{1}{12}\left(54+6\times 33^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{14}\pi +2\pi \text{, }n_{14}\in \mathrm{Z}$$

$$x=\pi +\left(-1\right)arcSin(\frac{1}{12}\left(54+6\times 33^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{19}\pi \text{, }n_{19}\in \mathrm{Z}$$

$$x=\pi +arcSin(\frac{1}{12}\left(54+\left(-6\right)\times 33^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{24}\pi \text{, }n_{24}\in \mathrm{Z}$$

$$x=arcSin(\frac{1}{12}\left(54+\left(-6\right)\times 33^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{29}\pi \text{, }n_{29}\in \mathrm{Z}$$

$$x=\frac{1}{6}\pi +2n_{9}\pi \text{, }n_{9}\in \mathrm{Z}$$

$$x=\frac{7}{6}\pi +2n_{10}\pi \text{, }n_{10}\in \mathrm{Z}$$