The area of a triangle with vertices (acosθ1,bsinθ1) and (acosθ2,bsinθ2) and(acosθ3,bsinθ3),(where  θ1≠θ2≠θ3) is equal to

Δ=12|acosθ1bsinθ11acosθ2bsinθ21acosθ3bsinθ31|    =12ab|cosθ1−cosθ2sinθ1−sinθ20cosθ2−cosθ3sinθ2−sinθ30cosθ3sinθ31|     =2absinθ1−θ22sinθ2−θ32    =2absinθ1−θ22sinθ2−θ32sinθ3−θ12