Let \( y=y(x) \) be solution of the following differential equation \( e^{y}\dfrac{dy}{dx}-2e^{y}\sin x+\sin x \cos^{2} x=0 , \; y\!\left(\dfrac{\pi}{2}\right)=0 \).
If \( y(0)=\log_{e}\!\left(\alpha+\beta e^{-2}\right) \), then \( 4(\alpha+\beta) \) is equal to____________ .
