(a)[2]
Show that the equation $\sin 2\theta + \cos 2\theta = 2\sin^2 \theta$ may be rewritten in the form $\cos^2 \theta + 2\sin \theta \cos \theta - 3\sin^2 \theta = 0$.
(b)[4]
Hence solve the equation $\sin 2\theta + \cos 2\theta = 2\sin^2 \theta$ for $0^\circ < \theta < 180^\circ$.