(1-√3tanθ)sec(θ+π/3)cosθ
=2*(1/2*cosθ-√3/2sinθ)/cosθ/cos(θ+π/3)*cosθ
=2(cos(π/3)cosθ-sin(π/3)sinθ)/cos(θ+π/3)
=2cos(θ+π/3)/cos(θ+π/3)
=2