Re-write arguments between $(-\pi,\pi]$ - why

Re-write arguments between $(-\pi,\pi]$ - why

I have a complex number answer with an argument of $4\pi/3$ and the
example said to make the argument a number between $(-\pi,\pi]$ however I
don't understand what that means or why we do it (the answer is
$-2\pi/3$).
On my unit circle graph there is no $-\pi$, so I can't find a number
between it and $\pi$. Furthermore I don't understand why we do that step.