(i) Prove the identity \(\frac{1 + \cos \theta}{1 - \cos \theta} - \frac{1 - \cos \theta}{1 + \cos \theta} \equiv \frac{4}{\sin \theta \tan \theta}\).

(ii) Hence solve, for \(0^\circ < \theta < 360^\circ\), the equation \(\sin \theta \left( \frac{1 + \cos \theta}{1 - \cos \theta} - \frac{1 - \cos \theta}{1 + \cos \theta} \right) = 3\).