For any $y \in \mathbb { R }$, let $\cot ^ { - 1 } ( y ) \in ( 0 , \pi )$ and $\tan ^ { - 1 } ( y ) \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$. Then the sum of all the solutions of the equation $\tan ^ { - 1 } \left( \frac { 6 y } { 9 - y ^ { 2 } } \right) + \cot ^ { - 1 } \left( \frac { 9 - y ^ { 2 } } { 6 y } \right) = \frac { 2 \pi } { 3 }$ for $0 < | y | < 3$, is equal to
(A) $2 \sqrt { 3 } - 3$
(B) $3 - 2 \sqrt { 3 }$
(C) $4 \sqrt { 3 } - 6$
(D) $6 - 4 \sqrt { 3 }$