(a) By writing \(3\theta = 2\theta+\theta\), show that \[ \cos 3\theta \equiv 4\cos^{3}\theta-3\cos\theta . \] (b) Hence solve, for \(0^\circ\le \theta \le 180^\circ\), \[ \cos 3\theta+\cos\theta\cos 2\theta=\cos^{2}\theta . \]