The function cotangent (cot) is undefined when the angle 0 is a multiple of π (pi) or 180 degrees, plus or minus any integer multiple of π/2 (pi/2).
In other words, cotangent is undefined when the angle 0 is equal to:
0° + 180°n, where n is an integer, or
π + πn/2, where n is an integer.
Therefore, there are infinitely many values of 0 for which cotangent is undefined.