Let y=y(x) be the solution of the differential equation cosec^2 x d y+2 d x=(1+y cos 2 x) cosec^2 x d x, with y((π)/4)=0. Then, the value of…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle \operatorname{cosec}^2 x \mathrm{~d} y+2 \mathrm{~d} x=(1+y \cos 2 x) \operatorname{cosec}^2 x \mathrm{~d} x$, with $\displaystyle y\left(\frac{\pi}{4}\right)=0$. Then, the value of $\displaystyle (y(0)+1)^2$ is equal to: