  We develop an algorithm solving the 3x3 real symmetric eigenproblem. This is
a common problem and in certain applications it must be solved many thousands
of times, see for example \cite{tripref} where each element in a finite element
grid generates one. Because of this it is useful to have a tailored method that
is easily coded and compact. Furthermore, the method described is fully
compatible with development as a GPU based code that would allow the
simultaneous solution of a large number of these small eigenproblems.
