Let $f : \left[ 0 , \frac { \pi } { 2 } \right] \rightarrow [ 0,1 ]$ be the function defined by $f ( x ) = \sin ^ { 2 } x$ and let $g : \left[ 0 , \frac { \pi } { 2 } \right] \rightarrow [ 0 , \infty )$ be the function defined by $g ( x ) = \sqrt { \frac { \pi x } { 2 } - x ^ { 2 } }$.\\
The value of $2 \int _ { 0 } ^ { \frac { \pi } { 2 } } f ( x ) g ( x ) d x - \int _ { 0 } ^ { \frac { \pi } { 2 } } g ( x ) d x$ is $\_\_\_\_$ .