If the sum of all the solutions of ${\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right) + {\cot ^{ - 1}}\left( {{{1 - {x^2}} \over {2x}}} \right) = {\pi \over 3}, - 1 < x < 1,x \ne 0$, is $\alpha - {4 \over {\sqrt 3 }}$, then $\alpha$ is equal to _____________.