In this paper, we provide an optimal search and detection tactic based on multiple look angles at the same target. It is assumed that the orientation of the target is uniform and the left hand side is the mirror image of the right hand side of the target. This is a multidimensional optimization problem that is generally known to be NP hard. In layman terms, it is computationally intensive to determine the optimal look angles. We make use of the principles of symmetry, elementary number theory analysis, and calculus to identify a set of critical look angles. From this set, we show that there is an optimal point which yields the maximum probability of detection. We also investigate another set of critical points and show that they are suboptimal when compared to the optimal solution. The results are simple, intuitive and easy to apply. We hope that this new tactic will modify the current protocol for conducting search and detection operations by intelligent agents.