In this paper, we analyze DS-CDMA/OFDM spectrum sharing system based on opportunistic spectrum access (OSA). In this system, the primary network air interface is based on DS-CDMA, in which the system performance is limited by a maximum total received interference. The total interference, among other things, is a function of the primary users' communication activity. In OSA, part of this interference is considered to be created by the secondary service, this portion is called interference threshold. Decreasing the activity of the primary users results in a higher interference threshold, and at the same time, creates less interference at the secondary service receiver; thus the achievable capacity of the secondary service is increased. In this paper, we analytically obtain the maximum achievable capacity of the secondary service over fading channel. Our analysis reveals the dependency of the achievable capacity and the users' activity in the primary network. A direct consequence of our analysis is that exploiting the temporal variations of the available radio resource caused by the users' activity in the primary network can significantly increase the maximum achievable capacity. Simulation results confirm our analysis.