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We consider spectrum sharing in a cognitive radio network where a secondary system co-exists with an automatic repeat-request (ARQ)-based primary system. A cooperate-and-access spectrum sharing protocol is proposed where the secondary system alternates between cooperation and access modes. In the cooperation mode, the secondary system serves as a relay to assist the primary transmission, and in return accumulates credits. The credits allow the secondary system to gain spectrum access by exploiting the ARQ retransmissions of the primary system. We show analytically that through the proposed credit system, as long as the credits accumulated in cooperation mode compensate for the degradation in primary performance during access mode, an equal or higher average throughput is achieved for the primary system than in the case without spectrum sharing, while providing spectrum access opportunities for the secondary system.