  The next generation of exoplanet space photometry missions proposed by both
NASA and ESA promise to discover small transiting planets around the nearest
and brightest main-sequence stars. The physical and rotational properties of
these stars, in conjunction with Gaia-precision distances, can be used to
determine the inclination of the stellar rotation axis. Given edge-on orbital
paths for transiting planets, stellar inclinations can be interpreted as
obliquities projected into the line of sight, which can be used to more clearly
reveal the system architectures of small planets and the factors that drive
their orbital evolution. To demonstrate the method, we use a sample of
simulated target stars for the NASA Transiting Exoplanet Survey Satellite
(TESS) mission. Based on predicted characteristics of these stars and likely
measurement uncertainties, we show that the expected TESS discoveries will
allow us to finely differentiate the true underlying obliquity distribution.
Under conservative assumptions in our illustrative example--in which the true
distribution is assumed to contain systems drawn from both well-aligned and
isotropic distributions (e.g., due to multiple migration channels)--the correct
fractions can be determined to within $0.15$, thus enabling constraints on the
evolutionary processes that shape system architectures. Moreover, because of
the excellent astrometric precision expected from Gaia, this technique will
also be applicable to the large number of planets already discovered by
${\textit Kepler}$ orbiting much more distant stars.
