Thus, Θ n in Eq. 120a is a function of the action variables {η n } (as we already expected from the expression in Eq. 103), and ϕ n in Eq. 120b is a function of the MMST angle variables {φ n }. In fact, using Eq. 75 and Eq. 54 (as well as the definition of η n in Eq. 122a), we have