For what values of theta is f (theta) = cot (theta) undefined

Cot (theta) = cos (theta) / sin (theta)

Assume the denominator is 0. If that's true, then sin (theta) = 0 leads to theta = 0 or theta = pi

Therefore, cot (theta) is undefined when theta = 0 or when theta = pi. This is assuming theta is restricted on the interval [0, 2pi)