Let $y=y(x)$ be solution of the following differential equation $e^y \frac{d y}{d x}-2 e^y \sin x+\sin x \cos ^2 x=0, y\left(\frac{\pi}{2}\right)=0$. If $y(0)=\log _0\left(\alpha+\beta e^{-2}\right)$ then $4(\alpha+\beta)$ is equal to $\_\_\_\_$ .
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