Question

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

Answer 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.