求助一道数列证明题

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\begin{eqnarray}
0<a_{1}<\sqrt{3}, a_{n+1} & = & a_{n}-\frac{\sin a_{n}}{n+1} \text {. 证明 } n a_{n}<\frac{3 a_{1}}{3-a_{1}^{2}}
\end{eqnarray}