arccot is defined for all real values of the argument except 0, i.e. it does NOT have a principal value in the same sense as arcsin or arccos, but the cot(120°) = -(1/3)√3 = cot(300°) ,etc.

arccot(x) always has a value between 0 and π, unless specified otherwise.

In order to understand better you should look at the graphs of arcsin and arccot along with the graphs of cot and sin. (You may need to put the graph of y=x in the same graphs!)