  Recent asteroseismic measurements have revealed a small population of stars
in close binaries, containing primaries with extremely slow rotation rates.
Such stars defy the standard expectation of tidal synchronization in such
systems, but they can potentially be explained if they are trapped in a
spin-orbit equilibrium known as Cassini state 2 (CS2). This state is maintained
by orbital precession due to an outer tertiary star, and it typically results
in a very sub-synchronous rotation rate and high degree of spin-orbit
misalignment. We examine how CS2 is affected by magnetic braking and different
types of tidal dissipation. Magnetic braking results in a slower equilibrium
rotation rate, while tidal dissipation via gravity waves can result in a
slightly higher rotation rate than predicted by equilibrium tidal theory, and
dissipation via inertial waves can result in much slower rotation rates. For
seven binary systems with slowly rotating primaries, we predict the location of
the outer tertiary predicted by the CS2 theory. In five of these systems, a
tertiary companion has already been detected, although it closer than expected
in three of these, potentially indicating tidal dissipation via inertial waves.
We also identify a few new candidate systems among a population of eclipsing
binaries with rotation measurements via spot modulation.
