Solve Theta^frac{5x-2{8}-3x-1/6}=x+1/6-1-x/3

$$\Theta ^ { \frac { 5 x - 2 } { 8 } - \frac { 3 x - 1 } { 6 } } = \frac { x + 1 } { 6 } - \frac { 1 - x } { 3 }$$

Solve for Θ (complex solution)

$$\Theta =e^{\frac{24\left(3Im(x)arg(-\frac{1-3x}{6})+3iRe(x)arg(-\frac{1-3x}{6})-2iarg(-\frac{1-3x}{6})\right)}{9\left(Re(x)\right)^{2}+9\left(Im(x)\right)^{2}-12Re(x)+4}-\frac{144iRe(x)\pi n_{1}}{9\left(Re(x)\right)^{2}+9\left(Im(x)\right)^{2}-12Re(x)+4}-\frac{144\pi n_{1}Im(x)}{9\left(Re(x)\right)^{2}+9\left(Im(x)\right)^{2}-12Re(x)+4}+\frac{96i\pi n_{1}}{9\left(Re(x)\right)^{2}+9\left(Im(x)\right)^{2}-12Re(x)+4}}\left(|\frac{1-3x}{6}|\right)^{\frac{24\left(-3iIm(x)+3Re(x)-2\right)}{9\left(Re(x)\right)^{2}+9\left(Im(x)\right)^{2}-12Re(x)+4}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for Θ

$$\left\{\begin{matrix}\Theta =-\left(\frac{x}{2}-\frac{1}{6}\right)^{\frac{24}{3x-2}}\text{, }&\left(x>\frac{1}{3}\text{ or }Denominator(\frac{24}{3x-2})\text{bmod}2=1\right)\text{ and }\left(x>\frac{1}{3}\text{ or }Numerator(\frac{x}{8}-\frac{1}{12})\text{bmod}2=1\right)\text{ and }x\neq \frac{1}{3}\text{ and }x\neq \frac{2}{3}\text{ and }Numerator(\frac{x}{8}-\frac{1}{12})\text{bmod}2=0\text{ and }Denominator(\frac{x}{8}-\frac{1}{12})\text{bmod}2=1\\\Theta =\left(\frac{x}{2}-\frac{1}{6}\right)^{\frac{24}{3x-2}}\text{, }&\left(x>\frac{1}{3}\text{ and }x\neq \frac{2}{3}\right)\text{ or }\left(Denominator(\frac{24}{3x-2})\text{bmod}2=1\text{ and }Numerator(\frac{x}{8}-\frac{1}{12})\text{bmod}2=1\text{ and }Denominator(\frac{x}{8}-\frac{1}{12})\text{bmod}2=1\text{ and }x<\frac{1}{3}\right)\end{matrix}\right.$$