Given that \(2 \sin \theta = 7 \cos \theta\), find the value of \(\tan \theta\).
Use an appropriate identity to show that the equation
$$6 \sin ^ { 2 } x = 4 + \cos x$$
can be written as
$$6 \cos ^ { 2 } x + \cos x - 2 = 0$$
Hence solve the equation \(6 \sin ^ { 2 } x = 4 + \cos x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\), giving your answers to the nearest degree.