Let \(f(\theta) = \frac{1 - \cos 2\theta + \sin 2\theta}{1 + \cos 2\theta + \sin 2\theta}\).

(i) Show that \(f(\theta) = \tan \theta\).

(ii) Hence show that \(\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} f(\theta) \, d\theta = \frac{1}{2} \ln \frac{3}{2}\).