Verified answer

Perhaps you are supposed to give an answer in the range [0,2π).

Use 11π/6 instead of -π/6.

Note that tan(5π/6) = tan(11π/6) = -1/√3

That is the answer. If you need an answer between [0,2pi] or [0,pi] then add pi to your answer.

-pi/6 + pi = 5pi/6

You're doing nothing wrong. Answer is correct.