Solution (source code)

= Solution

Interchanging the two wings gives
$$
\boxed{|\Psi_{RI}\rangle=-\frac12|\gamma\rangle+\frac1{2\sqrt2}\left(-|cc\rangle+i|cd\rangle+2i|dc\rangle\right).}
$$
Now detection at $D^-$ occurs only together with $C^+$, with <probability> $1/8$. The remaining nonzero coincidence probabilities are $P(C^+,C^-)=1/8$ and $P(D^+,C^-)=1/2$.