(a)[3]
Show that the equation $\tan(\theta + 60^\circ) = 2\cot\theta$ may be rearranged into the form $\tan^2\theta + 3\sqrt{3}\tan\theta - 2 = 0$.
(b)[3]
Hence solve the equation $\tan(\theta + 60^\circ) = 2\cot\theta$, for $0^\circ < \theta < 180^\circ$.