If cot α=1 and sec β=-5/3, where π<α<(3 π)/2 and (π)/2<β<π, then the value of tan (α+β) and the quadrant in which α+β lies, respectively are:

If $\displaystyle \cot \alpha=1$ and $\displaystyle \sec \beta=-\frac{5}{3}$, where $\displaystyle \pi<\alpha<\frac{3 \pi}{2}$ and $\displaystyle \frac{\pi}{2}<\beta<\pi$, then the value of $\displaystyle \tan (\alpha+\beta)$ and the quadrant in which $\displaystyle \alpha+\beta$ lies, respectively are :