If cosθ=cosαcosβ, then tanθ+α2tanθ−α2 is equal to

tanθ+α2tanθ−α2=tan2(θ/2)−tan2(α/2)1−tan2(θ/2)tan2(α/2)=1−cosθ1+cosθ−1−cosα1+cosα1−1−cosθ1+cosθ⋅1−cosα1+cosα=2(cosα−cosθ)2(cosα+cosθ)=cosα(1−cosβ)cosα(1+cosβ)=tan2β2