Dehn surgery on knots of wrapping number 2

Suppose K is a hyperbolic knot in a solid torus V intersecting a meridian disk D twice. We will show that if K is not the Whitehead knot and the frontier of a regular neighborhood of K ∪ D is incompressible in the knot exterior, then K admits at most one exceptional surgery, which must be toroidal. Embedding V in S gives infinitely many knots Kn with a slope rn corresponding to a slope r of K in V . If r surgery on K in V is toroidal then either Kn(rn) are toroidal for all but at most three n, or they are all atoroidal and nonhyperbolic. These will be used to classify exceptional surgeries on wrapped Montesinos knots in solid torus, obtained by connecting the top endpoints of a Montesinos tangle to the bottom endpoints by two arcs wrapping around the solid torus.