Three vertical poles of heights ${h}{1},{h}{2}$ and ${h}{3}$ at the vertices $A,B$ and $C$ of a $\triangle {ABC}$ subtend angles $\alpha ,\beta ,\gamma $ respectively at the circumcentre of the triangle. If $\cot { \alpha } ,\cot { \beta } ,\cot { \gamma } $ are in AP, then ${ h }{ 1 },{ h }{ 2 },{ h }{ 3 }$ are in