  We perform a comprehensive analysis of the superorbital modulation in the
ultracompact X-ray source 4U 1820-303, consisting of a white dwarf accreting
onto a neutron star. Based on RXTE data, we measure the fractional amplitude of
the source superorbital variability (with a 170-d quasi-period) in the folded
and averaged light curves, and find it to be by a factor of about 2. As
proposed before, the superorbital variability can be explained by oscillations
of the binary eccentricity. We now present detailed calculations of the
eccentricity-dependent flow through the inner Lagrangian point, and find a
maximum of the eccentricity of about 0.004 is sufficient to explain the
observed fractional amplitude. We then study hierarchical triple models
yielding the required quasi-periodic eccentricity oscillations through the
Kozai process. We find the resulting theoretical light curves to match well the
observed ones. We constrain the ratio of the semimajor axes of the outer and
inner systems, the component masses, and the inclination angle between the
inner and outer orbits. Last but not least, we discover a remarkable and
puzzling synchronization between the observed period of the superorbital
variability (equal to the period of the eccentricity oscillations in our model)
and the period of the general-relativistic periastron precession of the binary.
