I have this three-variable real function

$$ sin (x+y-z)+sin (x-y)+sin (x+z) , $$

where $-3<y,z<3$, **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.