If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors,show that : $(\overrightarrow{a}+\overrightarrow{b}).\{(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{c}+\overrightarrow{a})\}=2[\overrightarrow{a}\; \overrightarrow{b}\;\overrightarrow{c}]$