If $\overrightarrow a,\overrightarrow b \: and \overrightarrow c$are three mutually perpendicular vectors of equal magnitude, prove that the angle which $(\overrightarrow a+\overrightarrow b+\overrightarrow c)$ makes with any of the vectors $\overrightarrow a, \overrightarrow b \: or \overrightarrow c$ is $\cos^{-1}\large\frac{1}{\sqrt3}.$

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