  An assumption of isospin symmetry permits the determination of sin(2 alpha)
from the experimental study of B\to pi pi decays. Isospin, however, is merely
an approximate symmetry; its breaking predicates a theoretical systematical
error sigma_\alpha^{\rm IB} in the extraction of alpha. We focus on the impact
of \pi^0-\eta,\eta^\prime mixing, as well as the manner in which it is amenable
to empirical constraint, and determine that \sigma_\alpha^{\rm IB} can
potentially be controlled to {\cal O}(1^\circ).
