  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($\rm CF_4$) 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.
