=(1-cos40)/2+(1+cos160)/2+sqrt(3)/2(sin100-sin60)
=1-1/2cos40-1/2cos20-3/4+sqrt(3)/2sin100
=1/4-1/2(cos40+cos20)+sqrt(3)/2sin80
=1/4-cos10cos30+sqrt(3)/2sin80
=1/4-sqrt(3)/2cos10+sqrt(3)/2sin80
=1/4