  In this note, we combine the work of Ilmanen and of Colding-Ilmanen-Minicozzi
to observe a uniqueness property for tangent flows at the first singular time
of a smooth mean curvature flow of a closed surface in 3-dimensional Euclidean
space. Specifically, if, at a fixed singular point, one tangent flow is a
positive integer multiple of a shrinking plane, cylinder or sphere, then,
modulo rotations, all tangent flows at the point are the same.
