(a) Show that the equation \(\tan(\theta + 60^\circ) = 2 \cot \theta\) can be written in the form \(\tan^2 \theta + 3\sqrt{3} \tan \theta - 2 = 0\).

(b) Hence solve the equation \(\tan(\theta + 60^\circ) = 2 \cot \theta\), for \(0^\circ < \theta < 180^\circ\).