  Eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow
apsidal precession, below the rate predicted by the general relativity. Recent
measurements of the Rossiter-McLauglin effect indicate that stellar spins in DI
Her are almost orthogonal to the orbital angular momentum, which explains the
anomalous precession in agreement with the earlier theoretical suggestion by
Shakura. However, these measurements yield only the projections of the
spin-orbit angles onto the sky plane, leaving the spin projection onto our line
of sight unconstrained. Here we describe a method of determining the full
three-dimensional spin orientation of the binary components relying on the use
of the gravity darkening effect, which is significant for the rapidly rotating
stars in DI Her. Gravity darkening gives rise to nonuniform brightness
distribution over the stellar surface, the pattern of which depends on the
stellar spin orientation. Using archival photometric data obtained during
multiple eclipses spread over several decades we are able to constrain the
unknown spin angles in DI Her with this method, finding that spin axes of both
stars lie close to the plane of the sky. Our procedure fully accounts for the
precession of stellar spins over the long time span of observations.
