Let \( y=y(x) \) be the solution curve of the differential equation \( (1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0, \; y(0)=0 \). If the curve \( y=y(x) \) passes through the point \( \left(\alpha,-\frac{1}{2}\right) \), then a value of \( \alpha \) is:
\( \frac{\pi}{6} \)
\( \frac{\pi}{4} \)
\( \frac{\pi}{3} \)
\( \frac{\pi}{2} \)
