For any three vectors : $\overrightarrow a, \overrightarrow b \: and \: \overrightarrow c$ prove that $\bigg[ \overrightarrow a + \overrightarrow b \: \: \overrightarrow b + \overrightarrow c \: \overrightarrow c + \overrightarrow a \bigg] = 2 \bigg[ \overrightarrow a \: \overrightarrow b \: \overrightarrow c \bigg].$

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