(i) Express \((\sqrt{3}) \cos x + \sin x\) in the form \(R \cos(x - \alpha)\), where \(R > 0\) and \(0 < \alpha < \frac{1}{2}\pi\), giving the exact values of \(R\) and \(\alpha\).

(ii) Hence show that

\(\int_{\frac{1}{6}\pi}^{\frac{1}{2}\pi} \frac{1}{((\sqrt{3}) \cos x + \sin x)^2} \, dx = \frac{1}{4}\sqrt{3}.\)