Let \(y=y(x)\) be the solution curve of the differential equation \(\left(1+\sin x\right)\frac{dy}{dx}+\left(y+1\right)\…

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

[JEE Main 2026, 2 Apr (Shift 1)]