Let $y=y(x)$ be the solution of the differential equation

$\sec ^2 x d x+\left(e^{2 y} \tan ^2 x+\tan x\right) d y=0,0< x<\frac{\pi}{2}, y(\pi / 4)=0$.

If $y(\pi / 6)=\alpha$, then $e^{8 \alpha}$ is equal to ____________.