- (a) Express \(2 \cos \theta - \sin \theta\) in the form \(R \cos ( \theta + \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and give the value of \(\alpha\) to 2 decimal places.
(b) Hence solve, for \(0 \leqslant \theta < 360 ^ { \circ }\),
$$\frac { 2 } { 2 \cos \theta - \sin \theta - 1 } = 15$$
Give your answers to one decimal place.
(c) Use your solutions to parts (a) and (b) to deduce the smallest positive value of \(\theta\) for which
$$\frac { 2 } { 2 \cos \theta + \sin \theta - 1 } = 15$$
Give your answer to one decimal place.