(a)[4]
Prove that the identity $\frac{1 + \cos\theta}{1 - \cos\theta} - \frac{1 - \cos\theta}{1 + \cos\theta} = \frac{4}{\sin\theta \tan\theta}$ holds.
(b)[3]
Hence, for $0^\circ < \theta < 360^\circ$, solve $\sin\theta\left(\frac{1 + \cos\theta}{1 - \cos\theta} - \frac{1 - \cos\theta}{1 + \cos\theta}\right) = 3$.