Cognitive radio technology enables the coexistence of Primary (PUs) and Secondary Users (SUs) in the same spectrum. In this work, it is assumed that the PU implements a retransmission-based error control technique (ARQ). This creates an inherent redundancy in the interference created by primary transmissions to the SU. We investigate secondary transmission policies that take advantage of this redundancy. The basic idea is that, if a Secondary Receiver (SR) learns the Primary Message (PM) in a given primary retransmission, then it can use this knowledge to cancel the primary interference in the subsequent slots in case of primary retransmissions, thus achieving a larger secondary throughput. This gives rise to interesting trade-offs in the design of the secondary policy. In fact, on the one hand, a secondary transmission potentially increases the secondary throughput but, on the other, causes interference to the reception of the PM at the Primary Receiver (PR) and SR. Such interference may induce retransmissions of the same PM, which plays to the advantage of the secondary user, while at the same time making decoding of the PM more difficult also at the SR and reducing the available margin on the given interference constraint at the PR. It is proved that the optimal secondary strategy prioritizes transmissions in the states where the PM is known to the SR, due to the ability of the latter to perform interference mitigation and obtain a larger secondary throughput. Moreover, when the primary constraint is sufficiently loose, the Secondary Transmitter should also trasmit when the PM is unknown to the SR. The structure of the optimal policy is found, and the throughput benefit of the proposed technique is shown by numerical results.