The Brothers Ages

  NOTE: This puzzle is rated DIFFICULT. If you can't figure it out, don't feel bad.

There are three brothers. The product of their ages is 36.
The sum of their ages is equal to the age of their only sister.
The three brothers never admit their ages, but their sister always admits her own age.
Even so, you must know that the oldest brother usually wears his baseball cap backward.

How old is each brother?

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