Let $\mathit{a}$, $\mathit{b}$ and $\mathit{c}$ be three non-coplanar  vectors, and let $\mathit{p}$, $\mathit{q}$ and $\mathit{r}$ be the vectors defined by the  relations

$\mathbf{p}=\frac{\mathbf{b}\times \mathbf{c}}{\left[\mathbf{abc}\right]},\mathbf{q}=\frac{\mathbf{c}\times \mathbf{a}}{\left[\mathbf{abc}\right]}\text{ and }\mathbf{r}=\frac{\mathbf{a}\times \mathbf{b}}{\left[\mathbf{abc}\right]}$ Then the value of the expression $(\mathbf{a}+\mathbf{b})\cdot \mathbf{p}+(\mathbf{b}+\mathbf{c})\cdot \mathbf{q}$$+\left(\mathit{c}\mathbf{+}\mathit{a}\right) . \mathit{r}$ is equal to