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Little math behind that... The 3betting range you gave is ~12.4% of hands. The stack-off range is 3% of hands. So when faced with a 4bet, we can expect villain to call 3/12.4 or 24% of the time. Meaning he folds 76% of the time.
Assuming the action goes, we open 3x, he 3bets to 9x, and we 4bet to 24x, then we will be risking 21BB to win the 34.5BB pot (our 21 + our 3 + his 9 + 1.5 blinds). This raise has to work only 61% of the time to be profitable. And since we know without adjustments he is folding to 4bets 76% of the time, it will be profitable to 4bet bluff him, and often (until he adjusts).
So, as others said, 4bet the worst hands in your opening range, as they will be +EV based on fold equity alone in this spot, and flat his 3bet with the range you wish to continue with.
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