The angles that share the same tangent value as tan(45°) have terminal sides in quadrant IIIIIIV(none of the quadrants).

Since tan(45°) = 1, we need the quadrant where tangent is positive and an angle can have tangent 1. Tangent is positive in quadrants I and III; the angle with a 45° reference angle in quadrant III has tangent 1. The correct choice is III.

AI-written and checked against the verified answer.