When does cotangent equal -1?

cot[x]= -1

cot[x] = cos[x] / sin[x]

cos[x] / sin[x] = -1

cos[x] = -sin[x]

|cos[x]| = |sin[x]| at every multiple of Pi/4 + Pi/2. However, the signs disagree at 3Pi/4 + nPi, where n is an integer.