(a)[3]
Prove that $\frac{\sin \theta}{\sin \theta + \cos \theta} + \frac{\cos \theta}{\sin \theta - \cos \theta} = \frac{\tan^2 \theta + 1}{\tan^2 \theta - 1}$.
(b)[4]
Hence find the exact solutions of the equation $\frac{\sin \theta}{\sin \theta + \cos \theta} + $\frac{\cos \theta}{\sin \theta - \cos \theta} = 2$ when $0 \leq \theta \leq \pi$.