If a, b and c are non-zero vectors. The value of $a\cdot \left\{\right(b+c)\times (a+b+c\left)\right\}$ is _____________

$\begin{array}{l}\begin{array}{rl} & a\cdot \left\{\right(b+c)\times (a+b+c\left)\right\}\\ & \text{ or }a\cdot \left\{\right(b+c)\times a+(b+c)\times (b+c\left)\right\}\end{array}\\ \text{ or }a\cdot \left\{\right(b+c)\times a\}\\ \text{ But }(b+c)\times a\text{ is perpendicular to }a\text{. }\\ \therefore a\cdot \left\{\right(b+c)\times a\}=0\end{array}$