  We construct a Lagrangian in the cotangent bundle of a 3-torus whose
projection to the fiber is a neighborhood of a tropical curve with a single
4-valent vertex. This Lagrangian has an isolated conical singular point, and
its smooth locus is diffeomorphic to the minimally-twisted five component chain
link complement, a cusped hyperbolic 3-manifold. From this singular Lagrangian,
we construct an immersed Lagrangian, and determine when it is unobstructed in
the wrapped Fukaya category. We show, using quilted Floer theory, that for a
generic line in projective 3-space, there is a local system on this immersed
Lagrangian such that the resulting object of the wrapped Fukaya category is
homologically mirror to an object of the derived category supported on the
line.
