  Analysis of the transit light curve deformed by the stellar gravity darkening
allows us to photometrically measure both components of the spin-orbit angle
$\psi$, its sky projection $\lambda$ and inclination of the stellar spin axis
$i_\star$. In this paper, we apply the method to two transiting hot Jupiter
systems monitored with the Kepler spacecraft, Kepler-13A and HAT-P-7. For
Kepler-13A, we find $i_\star=81^\circ\pm5^\circ$ and $\psi=60^\circ\pm2^\circ$
adopting the spectroscopic constraint $\lambda=58.6^\circ\pm2.0^\circ$ by
Johnson et al. (2014). In our solution, the discrepancy between the above
$\lambda$ and that previously reported by Barnes et al. (2011) is solved by
fitting both of the two parameters in the quadratic limb-darkening law. We also
report the temporal variation in the orbital inclination of Kepler-13Ab,
$\mathrm{d} |\cos i_{\rm
orb}|/\mathrm{d}t=(-7.0\pm0.4)\times10^{-6}\,\mathrm{day}^{-1}$, providing
further evidence for the spin-orbit precession in this system. By fitting the
precession model to the time series of $i_{\rm orb}$, $\lambda$, and $i_\star$
obtained with the gravity-darkened model, we constrain the stellar quadrupole
moment $J_2=(6.1\pm0.3)\times10^{-5}$ for our new solution, which is several
times smaller than $J_2=(1.66\pm0.08)\times10^{-4}$ obtained for the previous
one. We show that the difference can be observable in the future evolution of
$\lambda$, thus providing a possibility to test our solution with follow-up
observations. The second target, HAT-P-7, is the first F-dwarf star analyzed
with the gravity-darkening method. Our analysis points to a nearly pole-on
configuration with $\psi=101^\circ\pm2^\circ$ or $87^\circ\pm2^\circ$ and the
gravity-darkening exponent $\beta$ consistent with $0.25$. Such an
observational constraint on $\beta$ can be useful for testing the theory of
gravity darkening.
