For three non–coplanar vectors \(\vec a,\vec b,\vec c\), if
\[
(\vec b+\vec c)\cdot\big((\vec c+\vec a)\times(\vec a+\vec b)\big)
= \alpha \,[\vec a\,\vec b\,\vec c]
\]
and
\[
(\vec a+\vec b)\cdot\big((\vec b+\vec c)\times(\vec a+\vec b+\vec c)\big)
= \beta \,[\vec a\,\vec b\,\vec c],
\]
then \(\alpha+\beta\) is equal to: