(i) Express \(5 \sin x + 12 \cos x\) in the form \(R \sin(x + \alpha)\), where \(R > 0\) and \(0^\circ < \alpha < 90^\circ\), giving the value of \(\alpha\) correct to 2 decimal places.

(ii) Hence solve the equation \(5 \sin 2\theta + 12 \cos 2\theta = 11\), giving all solutions in the interval \(0^\circ < \theta < 180^\circ\).