If (acosθi,asinθi),i=1,2,3  represent the vertices of an equilateral triangle inscribed in a circle , then

Given points lie in the circle x2+y2=a2  since the points are vertices of an equilateral  triangle∴  Circumcentre(0)  and centroid of triangle are same                     a3(cosθ1+cosθ2+cosθ3)=0  and a3(sinθ1+sinθ2+sinθ3)=0  ⇒cosθ1+cosθ2+cosθ3=0 and sinθ1+sinθ2+sinθ3=0and cosθ1+cosθ22 +sinθ1+sinθ22= -cosθ32+-sinθ32 =1⇒1+1+2cosθ1-θ2=1 ⇒cosθ1-θ2=-12