  The SO(3) instanton homology recently introduced by the authors associates a
finite-dimensional vector space over the field of two elements to every
embedded trivalent graph (or "web"). The present paper establishes a skein
exact triangle for this instanton homology, as well as a realization of the
octahedral axiom. From the octahedral diagram, one can derive equivalent
reformulations of the authors' conjecture that, for planar webs, the rank of
the instanton homology is equal to the number of Tait colorings.
