依题意，sinθ-√3·cosθ=8/5∴2sin(θ-π/3)=8/5∴sin(θ-π/3)=4/5∵θ∈(π/3，5π/6)∴θ-π/3∈(0，π/2)∴cos(θ-π/3)=3/5∴sin(2θ+π/3)=sin[2(θ-π/3)+π]=-sin[2(θ-π/3)]=-2sin(θ-π/3)cos(θ-π/3)=-24/25
