Verified answer

4cos(α/4)*cos((2π+α)/4)*cos((2π+α)/2) = 4cos(α/4)*cos(α/4+π/2)*cos(α/2+π) =

= 4cos(α/4)*(-sin(α/4))*(-cos(α/2)) = 4cos(α/4)*sin(α/4)*cos(α/2) =

= 2*[2*cos(α/4)*sin(α/4)]*cos(α/2) = 2*[sin(α/2)]*cos(α/2) = 2*sin(α/2)*cos(α/2) =  sin(α)