Let 0<θ<π2 be a fixed angle. If P(cosθ,sinθ) and Q(cos(α−θ),sin(α−θ)) the Q is obtained from P by

The points  P(cosθ,sinθ) and Q(cos(α−θ),sin(α−θ)) lies on the circle x2+y2=1clearly XOP=θXOQ=α−θIf OR be the bisector of angle POQ then ROQ=θ−(α−θ)2=θ−α2XOR=θ−α2−(θ−α)=α2⇒Slope of line OR is tanα2Thus Q is obtained from P by reflection in the line through origin with slope tanα2