(a)[3]
By writing $3\theta$ as $2\theta + \theta$, establish the identity $\cos 3\theta = 4\cos^3\theta - 3\cos \theta$.
(b)[5]
Hence solve the equation $\cos 3\theta + \cos \theta \cos 2\theta = \cos^2 \theta$ for $0^\circ \leq \theta \leq 180^\circ$.