Do I need to research chain of title for a tax deed?

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I am considering purchasing a tax deed on a foreclosed condo in Florida. I read a book on foreclosures that advised doing my own title research by doing a "chain of title" to check what owners could have a claim on the property. Is this necessary on a tax deed or should I not worry since the tax deed will wipe out the mortage liens?

If I do need to do a chain of title research, how far back should I go?

Right now I can see current owner and last sale to that owner, as well the mortgage deed for the previous owner.

thanks