Find the maximum angle $x$ in the range $0 ^ { \circ } \leq x \leq 360 ^ { \circ }$ which satisfies the equation
$$\cos ^ { 2 } ( 2 x ) + \sqrt { 3 } \sin ( 2 x ) - \frac { 7 } { 4 } = 0$$
A $30 ^ { \circ }$
B $60 ^ { \circ }$
C $120 ^ { \circ }$
D $150 ^ { \circ }$
E $210 ^ { \circ }$
F $240 ^ { \circ }$
G $300 ^ { \circ }$
H $330 ^ { \circ }$