已知sin（5π+a）=-五分之三,且a属于（2分之π,π）又tanβ=二分之一

sin(5π+a) = sin(4π+π+a) = -sina = -3/5
sina = 3/5
a属于（2分之π,π）
tana = -sina/√（1-sin^2a) = -(3/5)/(4/5) = -3/4
tanβ = 1/2
tan（a-β）= (tana - tanβ)/(1+tana tanβ) = (-3/4-1/2)/(1-3/8) = -2
cosa = -√(1-sin^2a) = -4/5
sin2a=2sinacosa=2*3/5*(-4/5) = -24/25
cos2a=1-2sin^2a=1-2*(3/5)^2 = 7/25
sin(2a+π/3)=sin2acosπ/3+cos2asinπ/3
= -24/25*1/2 + 7/25*√3/2
= (-24+7√3)/50