Revealing the nature of dark matter is one of the most interesting tasks in astrophysics. Measuring the distribution of recoil angles is said to be one of the most reliable methods to detect a positive signature of dark matter. We focused on measurements via spin-dependent interactions, and studied the feasibility with carbon tetrafluoride (CF4) gas, while taking into account the performance of an existing three-dimensional tracking detector. We consequently found that it is highly possible to detect a positive signature of dark matter via spin-dependent interactions. (C)\ 2003 Elsevier B.V. All rights reserved.