If sin^-1 \(\left(x-\frac{x^2}{2}+\frac{x^3}{4}-\ldots\right)\) + cos^-1 \(\left(x^2-\frac{x^4}{2}+\frac{x^6}{4}-\ldots \right)\) = \(\frac{\pi}{2}\) for 0 < |x| < \(\sqrt2\), then find the value of x.