Let 0<α<π/2 be a fixed angle. If P≡(cos⁡θ,sin⁡θ) and Q≡(cos⁡(α−θ),sin⁡(α−θ)), then Q is obtained from P by the

Clearly, points P(cos⁡θ,sin⁡θ) and Q(cos⁡(α−θ)sin⁡(α−θ) ) lie on circle of unit radius.  In the figure, ∠POX=θ and ∠QOX=α−θ . ∴ ∠QOP=α−2θ Now, ΔQOP is isosceles. Therefore, altitude or angle bisector OM is perpendicular bisector of PQ. ∠MOP=α−2θ2=α2−θ∠MOX=θ+α2−θ=α2Thus, point P is reflection of point Q inline OM having slope, tan α2