What is required in order to derive the expanding eigenvalues of Dr. Curt McMullen's torus orbifold bundles over the circle and the corresponding totally degenerate groups, as presented in Section 3.7 of his book, Renormalization and 3-Manifolds which Fiber over the Circle?

He provides this value for the orbifold bundle obtained from the torus with a singular point of order 2, but I cannot reproduce his method. I am eager to understand and, further, to derive the expanding eigenvalue for the orbifold bundle obtained from the torus with a singular point of order 3.

My inability to calculate these values is disconcerting because I am able to derive the values for the fixed points and the lengths of the singular closed geodesics analytically. My ambition is to have a coherent and comprehensive understanding of Dr. McMullen's work on the totally degenerate group which is isomorphic to the fundamental group of a 2-dimensional orbifold of genus 1 with a single cone point of order 3.

I believe that my fundamental problem is that I do not grasp the mathematical motivation for Dr. McMullen's reference for his work:

T. Jørgensen, "Compact 3-manifolds of constant negative curvature ﬁbering over the circle", Ann. of Math. (2) 106: 61–72 (1977).