Let \( y=y(x) \) be the solution of the differential equation \( \operatorname{cosec}{ }^{2} x d y+2 d x=(1+y \cos 2 x) …

Let \( y=y(x) \) be the solution of the differential equation

\( \operatorname{cosec}{ }^{2} x d y+2 d x=(1+y \cos 2 x) \operatorname{cosec} ^{2}x d x \), with

\( y\left(\frac{\pi}{4}\right)=0 \). Then, the value of \( (y(0)+1)^{2} \) is equal

to:

[JEE Main 2021, 22 Jul (Shift 2)]