- (a) Express \(\frac { 1 } { ( 1 + 3 x ) ( 1 - x ) }\) in partial fractions.
(b) Hence find the solution of the differential equation
$$( 1 + 3 x ) ( 1 - x ) \frac { \mathrm { d } y } { \mathrm {~d} x } = \tan y \quad - \frac { 1 } { 3 } < x \leqslant \frac { 1 } { 2 }$$
for which \(x = \frac { 1 } { 2 }\) when \(y = \frac { \pi } { 2 }\)
Give your answer in the form \(\sin ^ { n } y = \mathrm { f } ( x )\) where \(n\) is an integer to be found.