Differential Equations

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 ____________.