I think that ,if you did not study ligand field theory , it is example of octahedral complexes that are almost all diamagnetic, except of some fluorine complexes. If you have some other octahedral comlexes it will be a little diferent task.
Yes you should use ligand field theory, but in this case looks like to me that you shuold know only the fact that almost all Co(III) o. complexes are diamagnetic.
If you have more precise question and would like know why so it is just ask.