(i) Demonstrate that the equation \(\tan(60^\circ + \theta) + \tan(60^\circ - \theta) = k\) can be expressed in the form \((2\sqrt{3})(1 + \tan^2 \theta) = k(1 - 3\tan^2 \theta)\).

(ii) Solve the equation \(\tan(60^\circ + \theta) + \tan(60^\circ - \theta) = 3\sqrt{3}\), providing all solutions within the interval \(0^\circ \leq \theta \leq 180^\circ\).