Question 28
Let $\mathbf m=(\cos\theta)\mathbf i+(\sin\theta)\mathbf j$ and $\mathbf n=(\sqrt2-\sin\theta)\mathbf i+(\cos\theta)\mathbf j$, where $\mathbf i,\mathbf j$ are the usual unit vectors on the $x,y$ axes and $\pi\lt \theta\lt 2\pi$. If $|\mathbf m+\mathbf n|=8\sqrt2/5$, find $5\cos(\theta/2+\pi/8)+5$.