(a) Express \(4 \cos x - \sin x\) in the form \(R \cos(x + \alpha)\), where \(R > 0\) and \(0^\circ < \alpha < 90^\circ\). State the exact value of \(R\) and give \(\alpha\) correct to 2 decimal places.

(b) Hence solve the equation \(4 \cos 2x - \sin 2x = 3\) for \(0^\circ < x < 180^\circ\).