Question 5 - A-Level Maths

Prove the identity \(\frac { \cos \theta } { \tan \theta ( 1 - \sin \theta ) } \equiv 1 + \frac { 1 } { \sin \theta }\).
Hence solve the equation \(\frac { \cos \theta } { \tan \theta ( 1 - \sin \theta ) } = 4\), for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).