the answer is -pi/6
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root three over three is from a special triangle - the 30 60 90. √3/3 is the same as 1/√3. If you draw the special triangle, you can see that 1 and root three are the lengths of the two legs. Specifically, 1 is opposite pi/6 and √3 is adjacent to pi/6. Since tangent=opposite/adjacent, then tan(pi/6)=1/√3. So our reference angle is pi/6, but since we need to find -√3/3 then we need to find where tangent is negative. This happens in the second and fourth quadrants. The domain of tan inverse is from negative pi half to pi half so we will give the answer in the fourth quadrant, which is -pi/6.