# [Japt], 7 bytes

    p é ¤øU

[Try it online!][TIO-juvf5aqf]

             Implicit input, stored in variable 'U'
    p        U+U, "abcabc" -> "abcabcabcabc"
      é      Rotate 1 char to the right "abcabcabcabc" -> "cabcabcabcab"
        ¤    Remove first two chars, "cabcabcabcab" -> "bcabcabcab"
         øU  Check if U is in the above

[Japt]: https://github.com/ETHproductions/japt
[TIO-juvf5aqf]: https://tio.run/##y0osKPn/v0Dh8EqFQ0sO7wj9/z9aPTFRXYcLSEKopGQIgnCgYiBGrIJubhAA "Japt – Try It Online"