Consider three points P≡(−sin(β−α),−cosβ),Q≡(cos(β−α),sinβ),  and  R≡(cos(β−α+θ),sin(β−θ)), where 0<α,β,θ<π4. Then

P≡(−sin(β−α),−cosβ)≡(x1,y1)Q≡(cos(β−α),sinβ)≡(x2,y2)R≡(cos(β−α+θ),sin(β−θ))or R≡(x2cosθ+x1sinθ,y2cosθ+y1sinθ)If T≡(x2cosθ+x1sinθcosθ+sinθ,y2cosθ+y1sinθcosθ+sinθ), for some 'θ' then P,Q and T are collinear. ∴ P,Q,R are collinear if cosθ+sinθ=1, which is not possible as 0<θ<π4.Hence, P,Q,R are non-collinear.