  A first measurement of \fplus, the \CP-even content of the decay D->4pi using
decays of $\psi(3770)$ to quantum correlated $D\bar{D}$ decays collected by the
CLEO-c experiment is presented. The measured value is \fplus=$0.737 \pm 0.028$.
This relatively high value makes the decay mode particularly suitable for both
measurements of the CKM angle $\gamma$ and charm \CP-violation in a model
independent way. This novel approach to studying indirect \CP-violation in
charm decays is based on the time-dependent inclusive analysis of multi body
self-conjugate states. These final states can be used to determine the indirect
CP-violating observable $A_{\Gamma}$ and the mixing observable $y_{CP}$
provided that $F_+$ is known. This approach can yield significantly improved
sensitivity compared with the conventional method that relies on decays to
\CP~eigenstates.
