(a)[3]
Show that the equation $\frac{1}{\sin \theta + \cos \theta} + \frac{1}{\sin \theta - \cos \theta} = 1$ can be rewritten in the form $a\sin^2 \theta + b\sin \theta + c = 0$, where the constants $a$, $b$ and $c$ are to be determined.
(b)[3]
Hence solve the equation $\frac{1}{\sin \theta + \cos \theta} + \frac{1}{\sin \theta - \cos \theta} = 1$ for $0^\circ \leq \theta \leq 360^\circ$.