Conjecture on arguments of complex Markov triples

Let $(z_1,z_2,z_3)$ be an initial seed triple of roots of unity, and let $n$ be the minimal positive integer such that $z_i^n=1$ for each $i$. A triple of rational numbers $(a/n,b/n,c/n)$ whose entries sum to $1$ is called an admissible argument triple when it is realized as the arguments of a complex Markov triple. Conjecture on complex Markov arguments. Every triple $(a/n,b/n,c/n)$ that sums to $1$ is achieved as the argument of a complex Markov triple. Furthermore, if $(z_1,z_2,z_3)$ are irrational angles, then the image of the arguments of Markov triples is dense in the circle. This concerns the distribution of arguments in the complex Markov-number construction; the supplied text attributes the conjecture to GKW but gives no resolution, so its status remains open.