This paper studies the multicast capacity of full-duplex 1-2-1 networks. In this model, two nodes can communicate only if they point "beams" at each other; otherwise, no signal can be exchanged. The main result of this paper is that the approximate multicast capacity can be computed by solving a linear program in the activation times of links connecting pairs of nodes. This linear program has two appealing features: (i) it can be solved in polynomial-time in the number of nodes; (ii) it allows to efficiently find a network schedule optimal for the approximate capacity. Additionally, the relation between the approximate multicast capacity and the minimum approximate unicast capacity is studied. It is shown that the ratio between these two values is not universally equal to one, but it depends on the number of destinations in the network, as well as graph-theoretic properties of the network.