16. The tangent line to the curve $y = x + \ln x$ at the point $( 1,1 )$ is tangent to the curve $y = a x ^ { 2 } + ( a + 2 ) x + 1$. Then $a = $ $\_\_\_\_$ .
\section*{III. Solution Questions}
17 (This question is worth 12 points). In $\triangle A B C$, $D$ is a point on $BC$, $AD$ bisects $\angle B A C$, and $B D = 2 D C$.\\
(1) Find $\frac { \sin \angle B } { \sin \angle C }$;\\
(II) If $\angle B A C = 60 ^ { \circ }$, find $\angle B$.\\