  We show that the magneto-electric coupling in 3D (strong) topological
insulators is related to a second derivative of the bulk magnetization. The
formula we derive is the non-linear response analog of the Streda formula for
Hall conductivity (P. Streda, J. Phys. C: Solid State Physics, 15, 22 (1982)),
which relates the Hall conductivity to the derivative of the magnetization with
respect to chemical potential. Our finding allows one to extract the
magneto-electric coefficient by measuring the magnetization, while varying the
chemical potential and one more perturbing field. Such an experimental setup
could circumvent many of the current difficulties with measuring the
magneto-electric response in 3D topological insulators. The relation we find
also makes transparent the effect of disorder on the magneto-electric response,
which occurs only through the density of states, and has no effect when the
system is gapped.
