Let y be cot x.
The problem is now to solve
Between 0° and 180° the cot function is decreasing. So there is one and only one value verifying y=0 in this interval. And the function is pi(180)-periodic.
cot x = 0 when x=90° or 270° (because cot x = cos(x)/sin(x))
We know that and
By the property of the periodicity, too