(a) Express \(\sqrt{7} \sin x + 2 \cos x\) in the form \(R \sin(x + \alpha)\), 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 \(\sqrt{7} \sin 2\theta + 2 \cos 2\theta = 1\), for \(0^\circ < \theta < 180^\circ\).