If cot (theta) = 1.5 and theta is in quadrant 3, what is the value of sin theta

The answer:

cot (theta) = 1.5, to find theta, cot (theta) = 1.5 implies theta = arc cot (1.5)

but we kknow that cot (theta) = 1 / tan (theta), this implies

1 / tan (theta) = 1.5, and tan (theta) = 1 / 1.5 = 0.6

and theta is in quadrant 3, costheta and sintheta are negatives

so tan (theta) is positive,

tan (theta) = 0.6, therefore, (theta) = arctan (0.6) = 30.9°

finally (theta) = 30.9°