解方程组：sina=2sin(a/2)cos(a/2)=-4/5,sin(a/2)^2+cos(a/2)^2=1,构成：(sin(a/2)+cos(a/2))^2=1-4/5=1/5,
(sin(a/2)-cos(a/2))^2=1-(-4/5)=9/5,开方：因为a属于(π/2.3π/2),所以a/2属于(π/4.3π/4),此时sin(a/2)>cos(a/2),且（sin(a/2)+cos(a/2)）>0,所以：：sin(a/2)+cos(a/2）=√5/5,sin(a/2)-cos(a/2)=3√5/5,解得sin(a/2)=2√5/5,cos(a/2)=-√5/5,cos(a/2+π/3)=cos(a/2)cos(π/3)-,sin(a/2)sin(π/3)=(-√5/5)*1/2-(2√5/5)*(√3/2)=-(√5+2√15)/10.