5 The angle \(x\), measured in degrees, satisfies the equation
$$\cos \left( x - 30 ^ { \circ } \right) = 3 \sin \left( x - 60 ^ { \circ } \right)$$
- By expanding each side, show that the equation may be simplified to
$$( 2 \sqrt { } 3 ) \cos x = \sin x$$
- Find the two possible values of \(x\) lying between \(0 ^ { \circ }\) and \(360 ^ { \circ }\).
- Find the exact value of \(\cos 2 x\), giving your answer as a fraction.