  Suppose we put an $\epsilon$-disk around each lattice point in the plane, and
then we rotate this object around the origin for a set $\Theta$ of angles. When
do we cover the whole plane, except for a neighborhood of the origin? This is
the problem we study in this paper. It is very easy to see that if $\Theta =
[0,2\pi]$ then we do indeed cover. The problem becomes more interesting if we
try to achieve covering with a small closed set $\Theta$.
