Question 4 - A-Level Maths

Prove the identity \(( \sin \theta + \cos \theta ) ( 1 - \sin \theta \cos \theta ) \equiv \sin ^ { 3 } \theta + \cos ^ { 3 } \theta\).
Hence solve the equation \(( \sin \theta + \cos \theta ) ( 1 - \sin \theta \cos \theta ) = 3 \cos ^ { 3 } \theta\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).