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