  We measure the bulk system parameters of the seismically active,
rapidly-rotating $\delta$-Scuti KOI-976 and constrain the orbit geometry of its
transiting binary companion using a combined approach of asteroseismology and
gravity-darkening light curve analysis. KOI-976 is a
$1.62\pm0.2~\mathrm{M_\odot}$ star with a measured $v\sin(i)$ of $120\pm2$ km/s
and seismically-induced variable signal that varies by $\sim$ 0.6\% of the
star's total photometric brightness. We take advantage of the star's oblate
shape and seismic activity to perform three measurements of its obliquity angle
relative to the plane of the sky. We first apply rotational splitting theory to
the star's variable signal observed in short-cadence \emph{Kepler} photometry
to constrain KOI-976's obliquity angle, and then subtract off variability from
that dataset using the linear algorithm for significance reduction software
{\tt LASR}. We perform gravity-darkened fits to \emph{Kepler}
variability-subtracted short-cadence photometry and to \emph{Kepler's}
phase-folded long-cadence photometry to obtain two more measurements of the
star's obliquity. We find that the binary system transits in a grazing
configuration with measured obliquity values of $36^\circ\pm17^\circ$,
$46^\circ\pm16^\circ$, and $43^\circ\pm20^\circ$ respectively for the three
measurements. We perform these analyses as a way to demonstrate overcoming the
challenges high-mass stars can present to transit light curve fitting and to
prepare for the large number of exoplanets \emph{TESS} will discover orbiting
A/F stars.
