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Some 75% of the examples I've read are irrelevant. The trope isn't about the hero being a little weird. It's about a minor character. The Doctor is not an example. Even Jim Ignatowski is probably not an example.
If someone wants to write this example to be in example format, go ahead. Removed until then:
Deadpool is insane and aware he's in a comic book. Other characters don't or can't acknowledge him mentioning this.
If the habit of liking Anime doesn't get you, one of their songs will get stuck in your head! Japan Takes Over the World! That Wild Mass Guessing was right!
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How well does it match the trope?