  We prove that the restriction map from the subspace of regular points of the
holonomy perturbed SU(2) traceless flat moduli space of a tangle in a
3-manifold to the traceless flat moduli space of its boundary marked surface is
a Lagrangian immersion.
  A key ingredient in our proof is the use of composition in the Weinstein
category, combined with the fact that SU(2) holonomy perturbations in a
cylinder induce Hamiltonian isotopies. In addition, we show that $(S^2,4)$, the
2-sphere with four marked points, is its own traceless flat SU(2) moduli space.
