  In this paper we rigorously prove the existance of a non-trivial periodic
orbit for the non-linear delay differential equation: $x'(t) = K \sin(x(t-1))$
for $K=1.6$. We show that the equations on the Fourier equations have a
solution by computing the local Brower degree. This degree can be computed by
using a homotopy which validity can be checked by checking a finite number of
inequalities. Checking these inequalities is done by a computer program.
