Question 6 - A-Level Maths

Prove that \(\operatorname { cosec } 2 \theta - \cot 2 \theta \equiv \tan \theta\).
Hence show that \(\int _ { \frac { 1 } { 4 } \pi } ^ { \frac { 1 } { 3 } \pi } ( \operatorname { cosec } 2 \theta - \cot 2 \theta ) \mathrm { d } \theta = \frac { 1 } { 2 } \ln 2\).