(i)[4]
Show that the equation $\tan(60^\circ + \theta) + \tan(60^\circ - \theta) = k$ may be rearranged into the form $(2\sqrt{3})(1 + \tan^2 \theta) = k(1 - 3\tan^2 \theta)$.
(ii)[3]
Hence solve the equation $\tan(60^\circ + \theta) + \tan(60^\circ - \theta) = 3\sqrt{3}$, giving every solution in the interval $0^\circ \leq \theta \leq 180^\circ$.