$\displaystyle \alpha, \beta, \gamma$ are the angles of the top of a vertical tower from three distinct points A, B, and C, on a horizontal line that is on the same level as the base of the tower but does not necessarily pass through it. The distances AB=BC=d. Prove that the height h of the tower is given by

$\displaystyle h^2(\cot^2\alpha-2\cot^2\beta+\cot^2\gamma)=2d^2$

If $\displaystyle 2\cot\beta=\cot\alpha+\cot\gamma$, prove that the line ABC passes through the base of the tower.

I have already shown the h is given by $\displaystyle h^2(\cot^2\alpha-2\cot^2\beta+\cot^2\gamma)=2d^2$, but i don't how to prove that if $\displaystyle 2\cot\beta=\cot\alpha+\cot\gamma$ the line passes through the base of the tower.

Thanks for any help!