  Using the helicity formalism, we calculate the combined angular distribution
function of the two gamma photons ($\gamma_1$ and $\gamma_2$) and the electron
($e^-$) in the triple cascade process
$\bar{p}p\rightarrow{}^3D_3\rightarrow{}^3P_2+\gamma_1\rightarrow(\psi+\gamma_2)
+\gamma_1 \rightarrow (e^- + e^+) +\gamma_2 +\gamma_1$, when $\bar{p}$ and $p$
are arbitrarily polarized. We also derive six different partially integrated
angular distribution functions which give the angular distributions of one or
two particles in the final state. Our results show that by measuring the
two-particle angular distribution of $\gamma_1$ and $\gamma_2$ and that of
$\gamma_2$ and $e^-$, one can determine the relative magnitudes as well as the
relative phases of all the helicity amplitudes in the two charmonium radiative
transitions ${}^3D_3\rightarrow{}^3P_2+\gamma_1$ and $^3P_2\rightarrow
\psi+\gamma_2$.
