  Some fine differences between the twin $b$-flavored unitarity triangles are
calculated by means of a generalized Wolfenstein parametrization of the CKM
matrix, and a possibility of experimentally establishing the second triangle is
briefly discussed. We find that the apexes of these two triangles,
characterized respectively by $(\overline{\rho}, \overline{\eta})$ and
$(\widetilde{\rho}, \widetilde{\eta})$, are located on the same circular arc in
the complex plane. This observation provides us with a new way to test
consistency of the CKM picture of CP violation in the quark sector and probe
possible new physics. The differences between the apexes (i.e.,
$\widetilde{\rho} - \overline{\rho}$ and $\widetilde{\eta} - \overline{\eta}$)
are found to be of ${\cal O}(\lambda^2)$ with $\lambda \simeq 0.22$ being the
Wolfenstein expansion parameter, and the shapes of these two triangles are
found to be insensitive to the two-loop renormalization-group-equation running
effects up to the accuracy of ${\cal O}\left(\lambda^4\right)$.
