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I've been on most of the Radiance Class ships including Brilliance and I don't remember having any "Themed Nights", doesn't mean they don't have them though. Sorry. .... Neil.
I too cannot think of Themed Nights on any RCI I have been on.... Have you signed up for the meetandmingle - they may know more?
RCI don't do 'Themed' but Casual, Smart Casual & Formal are the dress codes, if that is what you mean't.