(i) Use the substitution \(x = \sin^2 \theta\) to show that \(\int \sqrt{\left( \frac{x}{1-x} \right)} \, dx = \int 2 \sin^2 \theta \, d\theta\).

(ii) Hence find the exact value of \(\int_0^{\frac{1}{4}} \sqrt{\left( \frac{x}{1-x} \right)} \, dx\).