  Given an edge-weighted metric complete graph with $n$ vertices, the maximum
weight metric triangle packing problem is to find a set of $n/3$
vertex-disjoint triangles with the total weight of all triangles in the packing
maximized. Several simple methods can lead to a 2/3-approximation ratio.
However, this barrier is not easy to break. Chen et al. proposed a randomized
approximation algorithm with an expected ratio of $(0.66768-\varepsilon)$ for
any constant $\varepsilon>0$. In this paper, we improve the approximation ratio
to $(0.66835-\varepsilon)$. Furthermore, we can derandomize our algorithm.
