Tedious $I$

Given , a $\triangle ABC$ which is $not-obtuse-angled$ .

Now a square , a regular polygon of sides $m$ and another regular polygon of sides $n$ are constructed on sides of given triangle.

$WLOG$ let angle $A=\alpha$ ,angle $B=\beta$ ,angle $C=\gamma$ . Such that $\alpha \leq \beta <\gamma$

Now centers of square and the 2 regular ploygons when joined form an $equilateral$ triangle .

Then find $m+n+ \alpha - \beta + \gamma$ .

Note : All angles are in degrees .