  Suppose that $\phi$ and $\psi$ are smooth complex-valued functions on the
circle that are invertible, have winding number zero with respect to the
origin, and have meromorphic extensions to an open neighborhood of the closed
unit disk. Let $T_\phi$ and $T_\psi$ denote the Toeplitz operators with symbols
$\phi$ and $\psi$ respectively. We give an explicit formula for the determinant
of $T_\phi T_\psi T_\phi^{-1} T_\psi^{-1}$ in terms of the products of the tame
symbols of $\phi$ and $\psi$ on the open unit disk.
