\begin{document}$ \delta^{(\alpha i)} = \arg [{ V_{\alpha 1} V_{\alpha 2} V_{\alpha 3} V_{1i} V_{2i} V_{3i} / V_{\alpha i }^{3} \det V }] $\end{document} for CP phases \begin{document}$ \delta^{(\alpha i)} $\end{document} associated with nine Euler-angle-like parameterizations of a flavor mixing matrix. Here, α and i denote the row and column carrying the trivial phases in a given parameterization. Furthermore, we show that the phases \begin{document}$ \delta^{(\alpha i)} $\end{document} and the nine angles \begin{document}$ \Phi_{\alpha i} $\end{document} of unitarity triangles satisfy compact sum rules \begin{document}$ \delta^{(\alpha, i+2)} - \delta^{(\alpha, i+1)} = \Phi_{\alpha+1, i} - \Phi_{\alpha+2, i} $\end{document} and \begin{document}$ \delta^{(\alpha+1, i)} - \delta^{(\alpha+2, i)} = \Phi_{\alpha, i+2} - \Phi_{\alpha, i+1} $\end{document} where all indices are taken cyclically modulo three. These relations are natural generalizations of the previous result \begin{document}$ \delta_{\mathrm{PDG}}+\delta_{\mathrm{KM}}=\pi-\alpha+\gamma. $\end{document}"> Rephasing invariant formulae for CP phases in general parameterizations of flavor mixing matrix and exact sum rules with unitarity triangles -
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