I’m not very good with the calculus of functions of two variables so I need someone to check my working below.

Prove that ifx,y,zare the interior angles of a triangle, then .

I decided to use calculus to prove the result, so I defined a function of two variables

So

Since , we must have .

Now

When ,

and

Hence f(x,y) has a maximum at , which is .

for all the anglesx,y,zof a triangle. Is my working all okay? ;)