TH-TMO 2018 Problem 4

Let $a, b, c$ be nonzero real numbers such that $a + b + c = 0$ . Determine the maximum possible value of $\frac{a^2b^2c^2}{ (a^2 + ab + b^2)(b^2 + bc + c^2)(c^2 + ca + a^2)}$ .