Let $$\vec{a}, \vec{b}, \vec{c}$$ be three vectors such that $$|\vec{a}| = \sqrt{31}$$, $$4|\vec{b}| = |\vec{c}| = 2$$ and $$2(\vec{a} \times \vec{b}) = 3(\vec{c} \times \vec{a})$$. If the angle between $$\vec{b}$$ and $$\vec{c}$$ is $$\dfrac{2\pi}{3}$$, then $$\left(\dfrac{\vec{a} \times \vec{c}}{\vec{a} \cdot \vec{b}}\right)^2$$ is equal to ______.