The non-zero real number $c$ is such that the equation $\cos x = c$ has two solutions for $0 < x < \frac { 3 } { 2 } \pi$. How many solutions of the equation $\cos ^ { 2 } 2 x = c ^ { 2 }$ are there in the range $0 < x < \frac { 3 } { 2 } \pi$ ?
..... 6
The non-zero real number $c$ is such that the equation $\cos x = c$ has two solutions for $0 < x < \frac { 3 } { 2 } \pi$.
How many solutions of the equation $\cos ^ { 2 } 2 x = c ^ { 2 }$ are there in the range $0 < x < \frac { 3 } { 2 } \pi$ ?