[tex]\bf y=cot^{-1}(x)\implies cot(y)=x\implies \cfrac{cos(y)}{sin(y)}=x[/tex]
now... that fraction, becomes undefined if the denominator becomes 0
when does that happen? well, it happens when sin(y) becomes 0, when is that?, notice your Unit Circle, that happens at 0, π, 2π, 3π and so on
now, on those angles, sin(y) is 0, and the rational of the cotangent, becomes undefined, so, therefore, those angles are NOT valid values for the angle, and outside the range.
now, just check for those, everyone else should be in the range.
