そのうち
before long, sooner or later
Somewhere inside that stretch of time, with nobody putting a date on it. The same Sonic その as その, and he will get there: そのうち.
もうすぐ is soon and means soon. その内 is vaguer, and can stretch to any time in the next twenty years.
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Emaki is not affiliated with, or endorsed by, Kaishi 1.5k or its authors. The word, reading and meaning come from the Kaishi 1.5k deck, used with their permission. The mnemonic, the note and the kanji breakdown are original work, published under CC BY-SA 4.0.