If
\[
y=\tan^{-1}\left[\left(\frac{1-\cos 2\sqrt{x}}{1+\cos 2\sqrt{x}}\right)^{\frac12}\right],
\qquad
0<x<\frac{\pi^2}{4},
\]
then \(y(2y'+y)=\)
Show Hint
Always remember the identity
\[
\frac{1-\cos2\theta}{1+\cos2\theta}=\tan^2\theta.
\]
Many inverse trigonometric problems collapse immediately after using this formula.