9 If the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}>0, a_{n}=\frac{a_{1}+a_{n-1}}{1-a_{1} a_{n-1}}(n \geqslant 2)$, and has the smallest positive period 2008, then $a_{1}=$ $\qquad$
(9) $\tan \frac{k \pi}{2008}$, positive integer $k \leqslant 1003$ and coprime with 2008.