The equation
$$\sin ^ { 2 } \left( 4 ^ { \cos \theta } \times 60 ^ { \circ } \right) = \frac { 3 } { 4 }$$
has exactly three solutions in the range $0 ^ { \circ } \leq \theta \leq x ^ { \circ }$
What is the range of all possible values of $x$ ?
A $90 \leq x < 120$
B $90 \leq x < 270$
C $120 \leq x < 240$
D $270 \leq x < 300$
E $\quad 300 \leq x < 360$
F $\quad 450 \leq x < 630$