Again, similar story to what you had before. The main part is to separate Re and Im pars of tan(Θ+i*Φ). If you do that you get
tan(α) = sin(2Θ)/(cos(2Θ)+cosh(2Φ))
sec(α) = sin(2Φ)/(cos(2Θ)+cosh(2Φ))
Next some manipulations with expressions you have.
Hint: e2Φ is basically coming from sinh(2Φ) and (or) cosh(2Φ). So try it.