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Is there any (known) embedding of the modular group $\text{PSL}(2,\mathbb{Z})$ into the outer automorphism group of a free group, $\text{Out}(F_n)$, where $n\ge 3$?

I'm sorry that the question is kind of out of nowhere. I'm studying the book on Geometric Group Theory by Bestvina-Sageev-Vogtmann, and trying to generalize some results; it's just a security check that I didn't make a goof.

I have very little knowledge in the theory of the modular group, but I know at least it has a free product structure, so is virtually free; and $\text{Out}(F_n)$ is a group with some kind of the Tits alternative. Thus I guess the answer may be quite straightforward.

There are well-known embeddings from $\text{PSL}(2,\mathbb{Z})$ to $\text{SL}(2,\mathbb{C})$ or some linear groups; but such representations are "linear", and I have no idea on the "free" representations...

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    Did you try something like this . Let $F(a,b,c)$ a free grouip on three generators, $A$ the automorphism of order two which permutes $a,b$; $B$ the automorphism of order 3 which is a cyclic permutation of $(a,b,c)$. Let $\psi$ a generic (iwip) automorphims of $F$. It is likely that, for $N$ large, the group generated by $A$, $\psi ^N B\psi^{-N}$ is a free product (isomorphic to $PSL(2,Z)$). – 2017-02-16
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    Thanks! That seems to naturally work. – 2017-02-16

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