已知6sina^2+sinacosa-2cosa^2=0,a属于【派/2，派】，求sin(2a+派/3)的值

6sina+sinacosa-2（cosa）^2=0可变为 (2sina-cosa)(3sina-cosa)=0 即2sina=cosa或3sina=-2cosa. (tana=1/2或-2/3) a属于[π/2,π),tana=-2/3 sina=2/√13,cosa=-3/√13 sin2a=2sinacoa=-12/13, cos2a=(coa)^2-(sina)^2=5/13 sin(2a+π/3)=sin2a