  DI Herculis is an eclipsing binary famous for a longstanding disagreement
between theory and observation of the apsidal precession rate, which was
resolved when both stars were found to be severely misaligned with the orbit.
We used data from the Transiting Exoplanet Survey Satellite (TESS) to refine
our knowledge of the stellar obliquities and sharpen the comparison between the
observed and theoretical precession rates. The TESS data show variations with a
1.07-day period, which we interpret as rotational modulation from starspots on
the primary star. This interpretation is supported by the detection of
photometric anomalies during primary eclipses consistent with starspot
crossings. The secondary eclipse light curve shows a repeatable asymmetry which
we interpret as an effect of gravity darkening. By combining the TESS data with
previously obtained data, we determined the three-dimensional spin directions
of both stars. Using this information, the updated value of the theoretical
apsidal precession rate (including the effects of tides, rotation, and general
relativity) is $1.35^{+0.58}_{-0.50}$ arcsec/cycle. The updated value of the
observed rate (after including new TESS eclipse times) is
$1.41^{+0.39}_{-0.28}$ arcsec/cycle. Given the agreement between the observed
and theoretical values, we fitted all the relevant data simultaneously assuming
the theory is correct. This allowed us to place tighter constraints on the
stellar obliquities, which are $75^{+3}_{-3}$ and $80^{+3}_{-3}$ degrees for
the primary and secondary stars, respectively.
