In this paper, we investigate the angle-domain spectrum opportunities of secondary users with directional transmission, and analyze the detection probability of spectrum holes. We also analyze the detection probability of interference allowed scenarios. By calculating the angle mean of spectrum holes, we get the mathematical statistical properties. Through the results of the numerical analysis in different scenarios, we demonstrate that when N is large enough (for example, N amp;#62; 10), the size of the angle delta has a dominant impact on the spectrum opportunity. Meanwhile, we prove that utilizing directional antennas and allowing interference can obtain more angle-domain spectrum opportunities and improve the spectrum utilization.