Question
How do I find $\arctan\left(\tan\left(\frac{2\pi}{3}\right)\right)$?
My thought process
So I first drew a right triangle on the 2nd quadrant as $\frac{\sqrt{3}}{2}$ and $-\frac{1}{2}$ as the legs of the triangles but then I get the answer as $-\sqrt{3}$ for tangent of the angle in the triangle that i drew and I dont know how to evaluate the arctan.
Best Answer
Points to remember:
$(1) $ The range of $\arctan $ is from $(-\frac {\pi}{2 },\frac {\pi}{2}) $.
$(2)$ We have $\tan \frac {2\pi}{3} =\tan (\pi-\frac {\pi}{3}) =-\tan\frac {\pi}{3} =\tan (-\frac {\pi}{3})$.
Hope you can take it from here.