Let a and b be two unit vectors such that the angle between them is (π)/4. If θ is the angle between the vectors ( a + b ) and ( a +2 b +2( a × b )),…

Let $\displaystyle \hat{\mathrm{a}}$ and $\displaystyle \hat{\mathrm{b}}$ be two unit vectors such that the angle between them is $\displaystyle \frac{\pi}{4}$. If $\displaystyle \theta$ is the angle between the vectors $\displaystyle (\hat{\mathrm{a}}+\hat{\mathrm{b}})$ and $\displaystyle (\hat{\mathrm{a}}+2 \hat{\mathrm{~b}}+2(\hat{\mathrm{a}} \times \hat{\mathrm{b}}))$, then the value of $\displaystyle 164 \cos ^2 \theta$ is equal to :