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This letter studies data rate fairness on the two-way relay channel. It analytically determines the optimal power values at both nodes and at the relay, that lead to a maximization of the sum rate under the fairness constraint. Amplify-and-Forward (AF) and Decode-and-Forward (DF) relaying protocols are considered. For AF, the optimization problem is turned into a single-variable convex optimization problem. For DF, rate balancing between Multiple Access and broadcast phases must be performed prior to setting nodes powers. Both optimized protocols are compared with reference AF and DF in terms of data rates through numerical simulations.