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We consider a cognitive radio network with an energy-harvesting secondary transmitter to improve both energy efficiency and spectral efficiency. The goal of this paper is to determine an optimal spectrum sensing policy that maximizes the expected total throughput subject to an energy causality constraint and a collision constraint. The energy causality constraint comes from the fact that the total consumed energy should be equal to or less than the total harvested energy, while the collision constraint is required to protect the primary user. We first show that the system can be divided into a spectrum-limited regime and an energy-limited regime depending on where the detection threshold for the spectrum sensor lies. Assuming infinite battery capacity, we derive the optimal detection threshold that maximizes the expected total throughput subject to the energy causality constraint and the collision constraint. Analytical and numerical results show that the system is energy-limited if the energy arrival rate is lower than the expected energy consumption for a single spectrum access. They also show that a decreasing probability of accessing the occupied spectrum does not always result in decreased probability of accessing the idle spectrum in the energy-limited regime.