(i)[3]
Prove that $\frac{1 + \cos \theta}{\sin \theta} + \frac{\sin \theta}{1 + \cos \theta} = \frac{2}{\sin \theta}$.
(ii)[3]
Hence solve the equation $\frac{1 + \cos \theta}{\sin \theta} + \frac{\sin \theta}{1 + \cos \theta} = \frac{3}{\cos \theta}$ for $0^\circ \leq \theta \leq 360^\circ$.