Question:

The number of real solutions of the equation <span class="math-inline">\(\sin^{-1}\left(\sum_{i=1}^{\infty} x^{i+1} - \sum_{i=1}^{\infty} \left(\frac{x}{2}\right)^{i}\right) = \frac{\pi}{2} - \cos^{-1}\left(\sum_{i=1}^{\infty} \left(\frac{x}{2}\right)^{i} - \sum_{i=1}^{\infty} (-x)^{i}\right)\)</span> lying in the interval <span class="math-inline">\(\left(\frac{1}{2}, \frac{1}{2}\right)\)</span> is ____