This paper proves that the angle of departure (AoD) estimation using the multiple signal classification (MUSIC) with only WiFi control frames for beamforming feedback (BFF), defined in IEEE 802.11ac/ax, is possible. Although channel state information (CSI) enables model-driven AoD estimation, most BFF-based sensing techniques are data-driven because they only contain the right singular vectors of CSI and subcarrier-averaged stream gain. Specifically, we find that right singular vectors with a subcarrier-averaged stream gain of zero have the same role as the noise subspace vectors in the CSI-based MUSIC algorithm. Numerical evaluations confirm that the proposed BFF-based MUSIC successfully estimates the AoDs and gains for all propagation paths. Meanwhile, this result implies a potential privacy risk; a malicious sniffer can carry out AoD estimation only with unencrypted BFF frames.