If $\vec{a}, \vec{b}, \vec{c}$ are noncoplanar, then the value of $\vec{a} \cdot \left\{ \frac{\vec{b} \times \vec{c}}{3\, \vec{b} \cdot (\vec{c} \times \vec{a})} \right\} \cdot \vec{b} - \left\{ \frac{\vec{c} \times \vec{a}}{3\, \vec{c} \cdot (\vec{a} \times \vec{b})} \right\}$ is …