Express \(5 \sin x + 12 \cos x\) in the form \(R \sin ( x + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), giving the value of \(\alpha\) correct to 2 decimal places.
Hence solve the equation
$$5 \sin 2 \theta + 12 \cos 2 \theta = 11$$
giving all solutions in the interval \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).