  A theta curve is a spatial embedding of the $\theta$-graph in the
three-sphere, taken up to ambient isotopy. We define the determinant of a theta
curve as an integer-valued invariant arising from the first homology of its
Klein cover. When a theta curve is simple, containing a constituent unknot, we
prove that the determinant of the theta curve is the product of the
determinants of the constituent knots. Our proofs are combinatorial, relying on
Kirchhoff's Matrix Tree Theorem and spanning tree enumeration results for
symmetric, signed, planar graphs.
