JEE Math Practice Question

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

1. A.$2 \sqrt{3}-3$
2. B.$3-2 \sqrt{3}$
3. C.$4 \sqrt{3}-6$
4. D.$6-4 \sqrt{3}$