$$\text{If } \alpha > \beta > \gamma > 0,\text{ then the expression}\cot^{-1}\!\left\{\beta+\frac{(1+\beta^2)}{(\alpha-\beta)}\right\} + \cot^{-1}\!\left\{\gamma+\frac{(1+\gamma^2)}{(\beta-\gamma)}\right\} + \cot^{-1}\!\left\{\alpha+\frac{(1+\alpha^2)}{(\gamma-\alpha)}\right\}\text{ is equal to:}$$

A

$$ \pi $$

B

$$ 0 $$

C

$$ \frac{\pi}{2} - (\alpha+\beta+\gamma) $$

D

$$ 3\pi $$