Question: Problem with Physics:-Define

Consider the following expression (omega being the socalled minimal spin connection in the vierbein formalism of general relativity):

with(Physics):
with(Tetrads):
omegaDef := omega[mu,c,d] = 1/2*(
   +e_[~rho,c]*(d_[mu](e_[rho,d]) - d_[rho](e_[mu,d]))
   -e_[~rho,d]*(d_[mu](e_[rho,c]) - d_[rho](e_[mu,c]))
)
-1/2*e_[~a,mu]*e_[~rho,c]*e_[~sigma,d]*(d_[rho](e_[sigma,a]) - d_[sigma](e_[rho,a]));
Define(omegaDef):

The Define command raises "Error, (in Physics:-Define) numeric exception: division by zero" in Schwarschild spacetime (loaded with g_[sc]), but not, say, in Tolman spacetime (loaded with g_[tolman]). Furthermore, if either the first two terms, or the last term, are/is removed in omega, then no error is raised in Schwarzschild spacetime. What is going on?