Work Step by Step
The value is not in the quadrant we want it to be in. When we refer back to the unit circle we see that $2\pi/3$ is in quadrant 2. Arctan isn't defined there unfortunately. So we look for a value for which tan's value stays the same but in the 4th or 1st quadrant. To do this, on your unit circle draw a line through $2\pi/3$ and the center and extend it so that it hits another point on the circle. When we do so we get $-\pi/3$.