In interpolation theory one is often confronted with the task of connecting two different points of data in a smooth and shortest possible way. On manifolds and in particular on Lie groups this translates to finding geodesics which connect two given points. For a special class of manifolds, called extrinsic symmetric spaces, one can show that in most cases, e.g., when the space is a semisimple Lie group, the wanted geodesics satisfy an endpoint geodesic formula. In this paper we derive two such formulas for the special Euclidean group in three dimensions, a non-semisimple case in which these formulas were unknown so far. Furthermore, closed form expressions are presented, which reproduce older results on endpoint geodesics.