  We show that the angle $\alpha_{ds}$ of the ``flattest'' unitarity triange
can be directly measured using the decays $\overline{B}_{d}\to \phi
\overline{K}^{(*)0}$ and $\overline{B}_{s}\to \phi{K}^{(*)0}$. Using both
$\overline{B}_{d}$ and $\overline{B}_{s}$ enables a further consistency test
since the expected time-dependent CP violating asymmetries are identical though
with opposite signs. Since large statistics of $\overline{B}_{d}$ and
$\overline{B}_{s}$ are needed for accurate measurements, FCC-ee and its
environment at the Z-pole is well suited for such studies. These measurements,
the precision of which could reach the sub-degree level, will contribute to
probe further the consistency of the CP sector of the Standard Model with
unprecedented level of accuracy. The main detector requirements that are set by
these measurements are also outlined.
