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)=sin2acosπ/3+cos2asinπ/3
=(5√13-12)/26