def phi_s(spin1x, spin1y, spin2x, spin2y):
    """ Returns the sum of the in-plane perpendicular spins."""
    phi1 = phi_from_spinx_spiny(spin1x, spin1y)
    phi2 = phi_from_spinx_spiny(spin2x, spin2y)
    return (phi1 + phi2) % (2 * numpy.pi)