Answer
$\frac{dy}{d\theta}=2\cot\theta$
Work Step by Step
$y=\ln{(\sin^2\theta})$
On differentiating both sides:
$\frac{dy}{d\theta}=\frac{d(\ln{(\sin^2\theta}))}{d\theta}$
$\frac{dy}{d\theta}=\frac{1}{\sin^2\theta}\frac{d({(\sin^2\theta}))}
{d\theta}$
$\frac{dy}{d\theta}=\frac{{(2\sin\theta\cos\theta})}{\sin^2\theta}=\frac{2\cos\theta}{\sin\theta}$
$\frac{dy}{d\theta}=2\cot\theta$
