We’ve got cuboid ABCDA’B’C’D’.

$\displaystyle \alpha$ = $\displaystyle \angle$ C’AB

$\displaystyle \beta$ = $\displaystyle \angle$ C’AD

$\displaystyle \gamma$ = $\displaystyle \angle$ C’AA’

Prove that:

tg $\displaystyle \alpha$ + tg $\displaystyle \beta$ +tg $\displaystyle \gamma$ ≤ $\displaystyle \frac {3}{2}$ tg $\displaystyle \alpha$ tg $\displaystyle \beta$ tg $\displaystyle \gamma$