If an abbreviation occurs at the end of sentence, is there one period or two? For example,
Caesar was assassinated in 44 B.C.. Brutus killed him.
Should there be one period or two?
This has nothing to do with etc.
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Only one. Chicago manual of style covers this (with various examples). Other style guides will usually agree (they don't on everything). In your case BC is quite often used without punctuation anyway.