  The first measurements of CP violation in the B system will probably extract
$\sin 2\alpha$, $\sin 2\beta$ and $\cos 2\gamma$. Assuming that the CP angles
$\alpha$, $\beta$ and $\gamma$ are the interior angles of the unitarity
triangle, this determines the angle set $(\alpha,\beta,\gamma)$ up to a twofold
discrete ambiguity. The presence of this discrete ambiguity can make the
discovery of new physics difficult: if only one of the two solutions is
consistent with constraints from other measurements in the B and K systems, one
is not sure whether new physics is present or not. I present examples of this
situation, and discuss ways to resolve the discrete ambiguity.
