multivariable calculus – How to prove the position of maximum of \$ sin (x+y-z)+sin (x-y)+sin (x+z) , \$?

I have this three-variable real function
$$sin (x+y-z)+sin (x-y)+sin (x+z) ,$$
where $$-3, but I do not know the range of $$x$$.

According to numerical data, I see that the maximum of this function happens at $$y=z=0$$ regardless of the value of $$x$$. How can I prove this by formula? Any hints are appreciated.