Let $\overrightarrow a$, $\overrightarrow b$, $\overrightarrow c$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $\theta$, with the vector $\overrightarrow a$ + $\overrightarrow b$ + $\overrightarrow c$. Then 36cos²2$\theta$ is equal to ___________.

$${\left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|^2} = {\left| {\overrightarrow a } \right|^2} + {\left| {\overrightarrow b } \right|^2} + {\left| {\overrightarrow c } \right|^2} + 2(\overrightarrow a \,.\,\overrightarrow b + \overrightarrow a \,.\,\overrightarrow c + \overrightarrow b \,.\,\overrightarrow c ) = 3$$<br><br>$$ \Rightarrow \left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right| = \sqrt 3 \overrightarrow a .(\overrightarrow a + \overrightarrow b + \overrightarrow c ) = \left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|\cos \theta $$<br><br>$\Rightarrow 1 = \sqrt 3 \cos \theta$<br><br>$\Rightarrow \cos 2\theta = - {1 \over 3}$<br><br>$\Rightarrow 36{\cos ^2}2\theta = 4$