sin(x+π/6)=1/3
sin(5π/6-x)=sin[π-(x+π/6)]=1/3
sin^2(π/3-x)=sin^2[π/2-(x+π/6)]=cos^2(x+π/6)=1-sin^2(x+π/6)=8/9
sin(5π/6-x)+sin^2(π/3-x)=1/3+8/9=11/9