There is a trivial $O(\frac{n^3}{T})$ time algorithm for approximate triangle counting where $T$ is the number of triangles in the graph and $n$ the number of vertices. At the same time, one may count triangles exactly using fast matrix multiplication in time $\tilde{O}(n^ω)$. Is it possible to get a negative dependency on the number of triangles $T$ while retaining the $n^ω$ dependency on $n$? We answer this question positively by providing an algorithm which runs in time $O\big(\frac{n^ω}{T^{ω- 2}}\big) \cdot \text{poly}(n^{o(1)}/ε)$. This is optimal in the sense that as long as the exponent of $T$ is independent of $n, T$, it cannot be improved while retaining the dependency on $n$; this as follows from the lower bound of Eden and Rosenbaum [APPROX/RANDOM 2018]. Our algorithm improves upon the state of the art when $T = ω(1)$ and $T = o(n)$. We also consider the problem of approximate triangle counting in sparse graphs, parameterizing by the number of edges $m$. The best known algorithm runs in time $\tilde{O}\big(\frac{m^{3/2}}{T}\big)$ [Eden et al., SIAM Journal on Computing, 2017]. There is also a well known algorithm for exact triangle counting that runs in time $\tilde{O}(m^{2ω/(ω+ 1)})$. We again get an algorithm that retains the exponent of $m$ while running faster on graphs with larger number of triangles. Specifically, our algorithm runs in time $O\Big(\frac{m^{2ω/(ω+1)}}{ T^{2(ω-1)/(ω+1)}}\Big) \cdot \text{poly}(n^{o(1)}/ε)$. This is again optimal in the sense that if the exponent of $T$ is to be constant, it cannot be improved without worsening the dependency on $m$. This algorithm improves upon the state of the art when $T = ω(1)$ and $T = o(\sqrt{m})$.