If vector a,b,c are three mutually perpendicular vectors equally inclined to vector a + b + c at angle θ, then find the value of 36 cos^2 2θ.

Question

If \(\vec{a} , \vec{b} , \vec{c} \) are three mutually perpendicular vectors equally inclined to\( \vec{a}+\vec{b}+\vec{c} \) at angle θ, then find the value of \(36 \cos^2 2\theta\)