  We present results of a unitary triangle fit based on the scan method. This
frequentist approach employs Gaussian uncertainties for experimental
quantities, but makes no arbitrary assumptions about the distribution of
theoretical errors. Instead, we perform a large number of fits, scanning over
regions of plausible theory errors for each quantity, and retain those fits
meeting a specific confidence level criterion, thereby constraining the $\bar
\rho - \bar \eta $ plane using the standard input measurements (CKM matrix
elements, $\sin2 \beta, B^0_{d,s}$ mixing, $\epsilon_K$) as well as branching
fraction and \CP asymmetry measurements of B decays to $PP, PV, VV$, and $a_1
P$ final states to determine $\alpha$, $D^{(*)}K^{(*)}$ modes to determine
$\gamma$, and $D^{(*)}\pi$ and $D\rho$ modes to determine $2\beta +\gamma$. We
parameterize individual decay amplitudes in terms of color-allowed tree,
color-suppressed tree, penguin, singlet penguin, electroweak penguin, as well
as $W$-exchange and $W$-annihilation amplitudes. With this parameterization, we
obtain a good fit to the measured branching fractions and \CP asymmetries
within the Standard Model {\it ansatz}, with no new physics contributions. This
simultaneous fit allows us to determine the correlation between $\alpha$ and
$\beta$ as well as between $\gamma$ and $\beta$.
