The number of real solutions of the equation $$\sin ^ { - 1 } \left( \sum _ { i = 1 } ^ { \infty } x ^ { i + 1 } - x \sum _ { i = 1 } ^ { \infty } \left( \frac { x } { 2 } \right) ^ { i } \right) = \frac { \pi } { 2 } - \cos ^ { - 1 } \left( \sum _ { i = 1 } ^ { \infty } \left( - \frac { x } { 2 } \right) ^ { i } - \sum _ { i = 1 } ^ { \infty } ( - x ) ^ { i } \right)$$ lying in the interval $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ is $\_\_\_\_$. (Here, the inverse trigonometric functions $\sin ^ { - 1 } x$ and $\cos ^ { - 1 } x$ assume values in $\left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$ and $[ 0 , \pi ]$, respectively.)