It might look strange, but it requires both periods if it is inside parentheses.
From The Chicago Manual of Style (17th ed.), 6.13 (the bold text is mine):
When an entire independent sentence is enclosed in parentheses or square brackets, the period belongs inside the closing parenthesis or bracket. When matter in parentheses or brackets, even a grammatically complete sentence, is included within another sentence, the period belongs outside . . . Avoid enclosing more than one complete sentence within another sentence. In the third example, two periods are required—one for the abbreviation etc. and one for the sentence as a whole, outside the parentheses . . .
Fiorelli insisted on rewriting the paragraph. (His newfound ability to type was both a blessing and a curse.)
Felipe had left an angry message for Isadora on the mantel (she noticed it while glancing in the mirror).
His chilly demeanor gave him an affinity for the noble gases (helium, neon, etc.).