Find all values of thetaθ , if thetaθ is in the interval [0degrees° , 360degrees° ) and has the given function value cot thetaθ=1

In the first quadrant, 0-90 degrees, the angle whose cotangent is is 45 degrees. The only other quadrant where cot theta is 1 is 3rd quadrant.

The 2 angles are 45 and 180+45 = 225 degrees

Answer 45, 225 degrees.