sin40(1+2sin10)
=sin40(1+2cos80)
=sin40(1+2(2cos^2 40-1)
=sin40(4cos^2 40-1)
=4sin40cos40cos40-sin40
=2sin80cos40-sin40
=2*(1/2)[sin(80+40)+sin(80-40)]-sin40
=sin120+sin40-sin40
=sin120
=sin60
=√3/2.