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

(ii) Hence solve the equation \(\frac{\cos \theta}{\tan \theta (1 - \sin \theta)} = 4\), for \(0^\circ \leq \theta \leq 360^\circ\).