Separating Different Models from Measuring $\alpha, \beta, \gamma$

New physics effects on the $B^0-\bar{B}^0$ mixing and B-decay amplitudes are discussed. By a combined analysis, the model of new physics can be partially distinguished.It is emphasized that the extraction of unitarity angles $\beta$ and $\gamma$ through rare decay $K\to \pi\nu\tilde{\nu}$ and charged B decay $B^{\pm}\to DK^{\pm}$ respectively is not likely to be affected by new physics. Such an observation could be used to distinguish the new physics effects from different mode ls. For instance, the top quark two-Higgs doublet model can be easily separated from those models without new phase in B-decay amplitudes, and can be further distinguished from the most general two Higgs doublet model by its absence of new phase in the $B^0-\bar{B}^0$ mixing.