Question 8 - A-Level Maths

Prove that \(\sin ^ { 2 } 2 \theta \left( \operatorname { cosec } ^ { 2 } \theta - \sec ^ { 2 } \theta \right) \equiv 4 \cos 2 \theta\).
Hence
(a) solve for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\) the equation \(\sin ^ { 2 } 2 \theta \left( \operatorname { cosec } ^ { 2 } \theta - \sec ^ { 2 } \theta \right) = 3\),
(b) find the exact value of \(\operatorname { cosec } ^ { 2 } 15 ^ { \circ } - \sec ^ { 2 } 15 ^ { \circ }\).