If `y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],`find`(dy)/(dx)`

Explanation

$$ \left.\left.y=\sin \left[2 \tan ^{-1}\{\sqrt{(}(1-x) / \sqrt{(} 1+x)\right)\right\}\right] $$
Put `x=\cos \theta`
$$
\begin{aligned}
&y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}\right\}\right] \\
&y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{2 \sin ^{2}(\theta / 2)}{2 \cos ^{2}(\theta / 2)}}\right\}\right] \\
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