Question 4 - A-Level Maths

Prove the identity \(\left( \frac { 1 } { \sin x } - \frac { 1 } { \tan x } \right) ^ { 2 } \equiv \frac { 1 - \cos x } { 1 + \cos x }\).
Hence solve the equation \(\left( \frac { 1 } { \sin x } - \frac { 1 } { \tan x } \right) ^ { 2 } = \frac { 2 } { 5 }\) for \(0 \leqslant x \leqslant 2 \pi\).