  We report that the electron spin relaxation time, T1, in a GaAs quantum dot
with a spin-1/2 ground state has a 180 degree periodicity in the orientation of
the in-plane magnetic field. This periodicity has been predicted for circular
dots as due to the interplay of Rashba and Dresselhaus spin orbit
contributions. Different from this prediction, we find that the extrema in the
T1 do not occur when the magnetic field is along the [110] and [1-10]
crystallographic directions. This deviation is attributed to an elliptical dot
confining potential. The T1 varies by more than an order of magnitude when
rotating a 3 Tesla field, reaching about 80 ms for the magic angle. We infer
from the data that in our device the sign of the Rashba and Dresselhaus
constants are opposite.
