Let \(y = y(x)\) be the solution of the differential equation \({\csc }^{2}\mathrm{xdy}+2\mathrm{dx}=(1+\mathrm{ycos}2\m…

Let \(y = y(x)\) be the solution of the differential equation \({\csc }^{2}\mathrm{xdy}+2\mathrm{dx}=(1+\mathrm{ycos}2\mathrm{x}){\csc }^{2}\mathrm{xdx}\), with \(\mathrm{y}\left(\frac{\pi }{4}\right)=0\). Then, the value of \((y(0) + 1)^2 \) is equal to:

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