- (a) Write \(\cos \theta + 4 \sin \theta\) in the form \(R \cos ( \theta - \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\). Give the exact value of \(R\) and give the value of \(\alpha\) in radians to 3 decimal places.
(b) Hence solve, for \(0 \leqslant \theta < \pi\), the equation
$$\cos 2 \theta + 4 \sin 2 \theta = 1.2$$
giving your answers to 2 decimal places.