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The model-independent method based on the triangle ideology is implemented to extract the CKM-matrix angle gamma in the decays of doubly heavy long-lived meson B_c. We analyze a color structure of diagrams and conditions to reconstruct two reference-triangles by tagging the flavor and CP eigenstates of D^0 meson in the fixed exclusive channels. The characteristic branching ratios are evaluated in the framework of QCD sum rules.

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