If cot theta is undefined, then what is the value of tan theta

If a function is undefined, this usually means that the value is 1 / 0.

Since tan theta is the reciprocal of cot theta. Therefore:

cot theta = 1 / 0 = 1 / tan theta

Taking the right side:

1 / 0 = 1 / tan theta

Rearranging so that tan theta is in the numerator:

tan theta = 0