  We study the phase of the transmission amplitude through a disordered quantum
dot in the Coulomb blockade regime. We calculate the phase dependence on gate
voltage for a disorder configuration. We show that over a ``period'',
consisting of a resonance and a transmission valley, the total phase change is
0 (mod $2\pi$). Deviations from this sum rule are small in the parameter (level
spacing/charging energy). The disorder-averaged phase-phase correlation
function is found showing interaction-induced correlations between phases at
different gate voltages.
