Question 8 - A-Level Maths

Prove the identity \(\frac { \sin 2 x } { 1 + \tan ^ { 2 } x } \equiv 2 \sin x \cos ^ { 3 } x\) 8
Hence find \(\int \frac { 4 \sin 4 \theta } { 1 + \tan ^ { 2 } 2 \theta } \mathrm {~d} \theta\)