Question 6 - A-Level Maths

Prove that \(2 \operatorname { cosec } 2 \theta \tan \theta \equiv \sec ^ { 2 } \theta\).
Hence
(a) solve the equation \(2 \operatorname { cosec } 2 \theta \tan \theta = 5\) for \(0 < \theta < \pi\),
(b) find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 6 } \pi } 2 \operatorname { cosec } 4 x \tan 2 x \mathrm {~d} x\).