If $\int \frac{\sin x}{\sin ^3 x+\cos ^3 x} d x=\alpha \log _e|1+\tan x|+\beta \log _e\left|1-\tan x+\tan ^2 x\right|+\gamma \tan ^{-1}\left(\frac{2 \tan x-1}{\sqrt{3}}\right)+c$, when $c$ is contant of integration, then the value of $18\left(\alpha+\beta+\gamma^2\right)$ is $\_\_\_\_$ .
