(a) Express $$\(\frac{1}{(1+3 x)(1-x)}\)$$ in partial fractions. (3) (b) Hence find the solution of the differential equation $$\[ (1+3 x)(1-x) \frac{\mathrm{d} y}{\mathrm{~d} x}=\tan y \quad-\frac{1}{3}< x \leqslant \frac{1}{2} \]$$ for which $$\(x=\frac{1}{2}\)$$ when $$\(y=\frac{\pi}{2}\)$$ Give your answer in the form $$\(\sin ^{n} y=\mathrm{f}(x)\)$$ where $$\(n\)$$ is an integer to be found. (6)

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