Let cos (α+β)=-1/10 and sin (α-β)=3/8, where 0<α<(π)/3 and 0<β<(π)/4. If tan 2 α=(3(1-r √ 5 ))/(√ 11 (s+√ 5 )), r, s ∈ N, then r+s is equal to ____.

Let $\displaystyle \cos (\alpha+\beta)=-\frac{1}{10}$ and $\displaystyle \sin (\alpha-\beta)=\frac{3}{8}$, where $\displaystyle 0<\alpha<\frac{\pi}{3}$ and $\displaystyle 0<\beta<\frac{\pi}{4}$. If $\displaystyle \tan 2 \alpha=\frac{3(1-r \sqrt{5})}{\sqrt{11}(s+\sqrt{5})}, r, s \in \mathbf{N}$, then $\displaystyle r+s$ is equal to $\displaystyle \_\_\_\_$.