You should be able to do this without a calculator, if you recognize the special triangle with angles 30,60 and 90 degrees.
It has sides 1,√3 and 2 correspondingly.
So what the question really says is, find x if tan x = -√3
from that special triangle, we know tan 60º=√3
so the angle in standard position is 60º
but x must be in the II or IV quadrants, so x = 120 or x = 300 degrees
or
x = 2pi/3 or 5pi/3 radians
Solve: x=Arctan(-sqrt3).
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