FP1 - Finding arguments in terms of pi

Hey guys. I'm currently stuck on the argument and modulus form. I do understand the modulus part, but I have absolutely no idea where you get arguments in terms of pie from.

Say:

arg z = arctan (1/ - square root of three) = -pie/6
Can you please explain to me where this -pie/6 came from? I would be eternally grateful! Thanks!!