Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice):

$$cos(ka)=cos(βb)cos(α(a−b))−\frac{α^2+β^2}{2αβ}sin(βb)sin(α(a−b))$$

I have been unsuccessful at calculating the determinant (also given on Wikipedia) despite multiple tries, and was unable to find literature which deals with the attractive variant of the potential.