Let \(I = \int_0^1 \frac{9}{(3 + x^2)^2} \, dx\).

(i) Using the substitution \(x = (\sqrt{3}) \tan \theta\), show that \(I = \sqrt{3} \int_0^{\frac{\pi}{6}} \cos^2 \theta \, d\theta\).

(ii) Hence find the exact value of \(I\).