If $y = y ( x )$ is the solution of the differential equation, $\sqrt { 4 - x ^ { 2 } } \frac { \mathrm {~d} y } { \mathrm {~d} x } = \left( \left( \sin ^ { - 1 } \left( \frac { x } { 2 } \right) \right) ^ { 2 } - y \right) \sin ^ { - 1 } \left( \frac { x } { 2 } \right) , - 2 \leq x \leq 2 , y ( 2 ) = \frac { \pi ^ { 2 } - 8 } { 4 }$, then $y ^ { 2 } ( 0 )$ is equal to