Let y=y(x) be the solution of the differential equation sec^2 x d x+(e^2 y tan^2 x+ tan x) d y=0,0<x<(π)/2, y(π / 4)=0. If y(π / 6)=α, then e^8 α is…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle \sec ^2 x d x+\left(e^{2 y} \tan ^2 x+\tan x\right) d y=0,0<x<\frac{\pi}{2}, y(\pi / 4)=0$. If $\displaystyle y(\pi / 6)=\alpha$, then $\displaystyle e^{8 \alpha}$ is equal to $\displaystyle \_\_\_\_$.