If the sum of all the solutions of tan^-1((2 x)/(1-x^2))+ cot^-1((1-x^2)/(2 x))=(π)/3,-1<x<1, x ≠ 0, is α-4/(√ 3), then α is equal to ____.

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