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Consider https://en.wikipedia.org/w/index.php?title=Triiodide&oldid=704463427 or similar. The oxidation state of -1/3 for the iodine atoms in your product is an average, just as e.g. in propane the oxidation state of carbon is probably formally +8/3.Oxidation numbers are useful in some instances (like here) but less so in others.
2/3 is a number of electrons moved for 1 iodine atom. but I3- you have 3 atoms then number of moved electrons in reaction is 3·(2/3)=2.Mean oxidation number for I in I3- is 1/3