Final answer:
The archaic second-person pronoun used before "gods" in an expletive is "Thee". It is an older form of 'you' and is seldom used in modern English except in historical or literary references.
Step-by-step explanation:
The archaic second-person pronoun found before "gods" in a mild expletive is: a) Thee. The mild expletive in this context might be something like "By thee gods!" or "For thee gods!" The use of "thee" is an archaic form of the second-person singular, often used in addressing or referring to a person with familiarity or respect. In this construction, "thee gods" implies an appeal or expression directed towards divine entities. While "thou" and "thy" are also archaic second-person pronouns, "thee" is the correct choice for this specific construction. "Tho" is a more modern abbreviation and is not the archaic form used in this context.