  Measurements of the coherence factor $R_{K3\pi}$, the average strong-phase
difference $\delta^{K3\pi}_D$ and mean amplitude ratio $r_D^{K3\pi}$ for the
decay $D \to K^-\pi^+\pi^+\pi^-$ are presented. These parameters are important
inputs to the determination of the unitarity triangle angle $\gamma$ in $B^-
\to DK^-$ decays, where $D$ designates a superposition of $D^0$ and
$\bar{D}{}^0$ mesons decaying to a common final state. The results are based on
a combined fit to observables obtained from a re-analysis of the CLEO-c
$\psi(3770)$ data set and those measured in a $D^0\bar{D}^0$ mixing study
performed by the LHCb collaboration.
