Yes, 1...Rxe3 is a good move.
However, after the forced line
1...Rxe3 2 fxe3 Bxe3 3 Qxe3 Rxe3 4 Rxd7 Rxf3 5 Rxf7 Rxf7 6 Rf1 Qe4 7 Rxf7 Qe1+ 8 Kc2 Kh7
black has a queen (9) for a rook and a bishop (5 + 3 = 8), definitely an advantage, but hard to convert to a win.
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I'm not sure if I should post this in Game Analysis or Puzzles, but I'm posting it in Game Analysis because I want to talk about the specific strategy I had. Below is what I thought was a great rook-sacrifice situation: