Wolfram Alpha evaluates $\operatorname{arccot}(-\sqrt{3}/3)$ as $-\pi/3$ instead of $2\pi/3$

Question

Evaluating $$\operatorname{arccot}(-\sqrt{3}/3)$$

I tried this in Wolfram Alpha trying to verify a solution of mine, and I was expecting to get $2 \pi / 3$ but it says $-\pi/3$.

Does it consider the range of $\operatorname{arccot}$ something different than the usual $(0, \pi)$?

If so... isn't it causing quite some confusion?