  We compute the action-angle variables for a Hamiltonian flow of the
inhomogeneous six-vertex model, from a formulation introduced in a 2022 work
due to Keating, Reshetikhin, and Sridhar, hence confirming a conjecture of the
authors as to whether the Hamiltonian flow is integrable. To demonstrate that
such an integrability property of the Hamiltonian holds from the action-angle
variables, we make use of previous methods for studying Hamiltonian systems,
implemented by Faddeev and Takhtajan, in which it was shown that integrability
of a Hamiltonian system holds for the nonlinear Schrodinger's equation by
computing action-angle variables from the Poisson bracket, which is connected
to the analysis of entries of the monodromy and transfer matrices. For the
inhomogeneous six-vertex model, an approach for computing the action-angle
variables is possible through formulating several relations between entries of
the quantum monodromy, and transfer, matrices, which can be not only be further
examined from the structure of $L$ operators, but also from computing several
Poisson brackets parameterized from entries of the monodromy matrix.
