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