6(sina)^2+sina*cosa-2(cosa)^2=0
(3sina+2cosa)(2sina-cosa)=0
3sina+2cosa=0或者2sina-cosa=0
tana=-2/3或者tana=1/2
因为α属于[π/2,π）
所以tana<0
tana=-2/3
sina=2/根号13 cosa=-3/根号13
sin(2a)=-12/13 cos2a=5/13
sin(2a+π/3)=sin(2a)*cosπ/3+cos(2a)*sinπ/3
=-12/13*1/2+5/13*根号3/2
=(5根号3-12)/26