The number of solutions of the equation ${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}$, for x$\in$[$-$1, 1], and [x] denotes the greatest integer less than or equal to x, is :