We present for the first time a measurement of the weak phase 2b+g obtained from a time-dependent Dalitz plot analysis of B^0 -> D-(+) K0 Pi+(-) decays. Using a sample of approximately 347*10^{6} BBbar pairs collected by the BABAR detector at the PEP-II asymmetric-energy storage rings, we obtain 2b+g = (83 +/- 53 +/- 20) degrees and (263 +/- 53 +/- 20) degrees assuming the ratio r of the b -> u and b -> c decay amplitudes to be 0.3. The magnitudes and phases for the resonances associated with the b -> c transitions are also extracted from the fit.
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