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