Express \(3 \sin 2 \theta \sec \theta + 10 \cos \left( \theta - 30 ^ { \circ } \right)\) in the form \(R \sin ( \theta + \alpha )\) where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the value of \(\alpha\) correct to 2 decimal places.
Hence solve the equation \(3 \sin 4 \beta \sec 2 \beta + 10 \cos \left( 2 \beta - 30 ^ { \circ } \right) = 2\) for \(0 ^ { \circ } < \beta < 90 ^ { \circ }\).
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