  [Abridged] The recent discovery of a transiting planet on a non-circular
orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the
possibility of probing the structure of the short-period planet. The ability to
do this relies on the system being in a quasi-equilibrium state in the sense
that the eccentricities are constant on the usual secular timescale, and decay
on a timescale which is much longer than the age of the system. Since the
equilibrium eccentricity is effectively a function only of observable system
parameters and the unknown Love number of the short-period planet, the latter
can be determined with accurate measurements of the planet's eccentricity and
radius. However, this analysis relies on the unlikely assumption that the
system is coplanar. Here we generalize our recent analysis of this fixed-point
phenomenon to mutually inclined systems and show that the fixed point of
coplanar systems is replaced by a limit cycle, with the average value of the
eccentricity decreasing and its amplitude of variation increasing with
increasing mutual inclination. This behaviour significantly reduces the ability
to unambiguously determine the Love number of the short-period planet if the
mutual inclination is higher than around 10^o. We show that for Q-values less
than 10^6, the HAT-P-13 system cannot have a mutual inclination between 54 and
126^o because Kozai oscillations coupled with tidal dissipation would act to
quickly move the inclination outside this range, and that the behaviour of
retrograde systems is the mirror image of that for prograde systems. We derive
a relationship between the equilibrium radius of the short-period planet, its
Q-value and its core mass, and show that given current estimates of e_b and the
planet radius, the HAT-P-13 system is likely to be close to coplanar [...]
