An isomer counter and mirror plane tester

You will write three functions. One lists the distinct sets of trans pairs of an octahedral complex with monodentate ligands. One tests for a mirror plane. One counts the geometrical isomers and the stereoisomers.

The idea. A set of trans pairs is a geometrical isomer. A mirror plane exists if one pair is two identical ligands or two pairs are the same. A chiral isomer counts twice among the stereoisomers.

Your tasks.

1. Complete trans_pairs(ligands) so that it returns a sorted list of the different sets of three trans pairs.
2. Complete has_mirror_plane(pairs) so that it returns True when the rule is met.
3. Complete counts(ligands) so that it returns the pair (geometrical, stereoisomers).