Question 6
Let the angles of a triangle be $\alpha$, $\beta$, and $\gamma$, the perimeter $2p$ and the radius of the circumcircle $R$. Prove the inequality
$$
cot^2 \alpha + cot^2 \beta + cot^2 \gamma \ge 3 \left( \frac{9R^2}{p^2} - 1 \right).
$$
When is the equality achieved?
$$
cot^2 \alpha + cot^2 \beta + cot^2 \gamma \ge 3 \left( \frac{9R^2}{p^2} - 1 \right).
$$
When is the equality achieved?