4 By using an integrating factor, find the solution of the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } + ( \cot x ) y = \sin 2 x , \quad 0 < x < \frac { \pi } { 2 }$$ given that \(y = \frac { 1 } { 2 }\) when \(x = \frac { \pi } { 6 }\).
(10 marks)