Let y=y(x) be solution of the following differential equation e^y (d y)/(d x)-2 e^y sin x+ sin x cos^2 x=0, y((π)/2)=0. If y(0)= log_e (α+β e^-2),…

Let $\displaystyle y=y(x)$ be solution of the following differential equation $\displaystyle \mathrm{e}^y \frac{\mathrm{~d} y}{\mathrm{~d} x}-2 \mathrm{e}^y \sin x+\sin x \cos ^2 x=0, y\left(\frac{\pi}{2}\right)=0$. If $\displaystyle y(0)=\log _{\mathrm{e}}\left(\alpha+\beta \mathrm{e}^{-2}\right)$, then $\displaystyle 4(\alpha+\beta)$ is equal to \_\_\_\_.