(i) Express \(\frac{2}{(x+1)(x+3)}\) in partial fractions.

(ii) Using your answer to part (i), show that \(\left( \frac{2}{(x+1)(x+3)} \right)^2 \equiv \frac{1}{(x+1)^2} - \frac{1}{x+1} + \frac{1}{x+3} + \frac{1}{(x+3)^2}\).

(iii) Hence show that \(\int_0^1 \frac{4}{(x+1)^2(x+3)^2} \, dx = \frac{7}{12} - \ln \frac{3}{2}\).