  We compute the 1-loop partition function for strings in
$AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp
angles in the boundary of AdS. We obtain these 1-loop results in terms of the
vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz
and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to
the next to leading order in the strong coupling expansion. The agreement is
observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
