Vector Product of Four Vectors

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three non-coplanar non-zero vectors and $\overrightarrow{\mathit{r}}$ is any vector in space, then $\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left(\overrightarrow{r}\times \overrightarrow{c}\right)+\left(\overrightarrow{b}\times \overrightarrow{c}\right)\times \left(\overrightarrow{r}\times \overrightarrow{a}\right)+\left(\overrightarrow{c}\times \overrightarrow{a}\right)\times \left(\overrightarrow{r}\times \overrightarrow{b}\right)$ is equal to

For unit vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ and any non-zero vector $\overrightarrow{a}$, the value of $\left\{\left(\overrightarrow{a}+\overrightarrow{b}\right)\times \left(\overrightarrow{a}+\overrightarrow{c}\right)\}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)\right\}·\left(\overrightarrow{b}+\overrightarrow{c}\right)$ is

For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}; \left(\overrightarrow{b}\times \overrightarrow{c}\right)\times \left(\overrightarrow{c}\times \overrightarrow{a}\right)=$