(i)[2]
Find the derivative of $\frac{1}{\sin^2 \theta}$ with respect to $\theta$.
(ii)[6]
The variables $x$ and $\theta$ satisfy the differential equation $x \tan \theta \frac{dx}{d\theta} + \cosec^2 \theta = 0$, for $0 < \theta < \frac{1}{2}\pi$ and $x > 0$. It is given that $x = 4$ when $\theta = $\frac{1}{6}\pi$. Solve the differential equation, finding $x$ as a function of $\theta$.