Express \(2 \sin x + \cos x\) in the form \(R \sin ( x + \alpha )\) where \(R\) is a positive constant and \(\alpha\) is an acute angle. Give your value of \(\alpha\) to the nearest \(0.1 ^ { \circ }\).
Solve the equation \(2 \sin x + \cos x = 1\) for \(0 ^ { \circ } \leqslant x < 360 ^ { \circ }\).