3/(sin20)^2 - 1/(cos20)^2 + 64(sin20)^2
=[3(cos20)^2-(sin20)^2]/(sin20cos20)^2 + 64(sin20)^2
=[(3/4)(cos20)^2-(1/4)(sin20)^2]/[(sin20cos20)^2/4] + 64(sin20)^2
=[(√3/2)cos20+(1/2)sin20][(√3/2)cos20-(1/2)sin20]/[(sin40)^2/16] + 32*[2(sin20)^2]
=16cos(30-20)cos(30+20)/(sin40)^2 + 32[2(sin20)^2-1+1]
=16sin80sin40/(sin40)^2 + 32*(-cos40+1)
=32cos40(sin40)^2/(sin40)^2 - 32cos40 +32
=32cos40 - 32cos40 +32
=32