If $\theta =\frac{\pi }{21}$, then $\frac{\sin 23\theta -\sin 7\theta }{\sin 2\theta +\sin 14\theta }=$

$\theta =\frac{\pi }{21}$

$\frac{\sin 23\theta -\sin 7\theta }{\sin 2\theta +\sin 14\theta }$

$=\frac{\sin \frac{23\pi }{21}-\sin \frac{7\pi }{21}}{\sin \frac{2\pi }{21}+\sin \frac{14\pi }{21}}$

$=\frac{\sin (\pi +\frac{2\pi }{21})-\sin \frac{\pi }{3}}{\sin \frac{2\pi }{21}+\sin (\pi -\frac{\pi }{3})}$

$=\frac{-\sin \frac{2\pi }{21}-\sin \frac{\pi }{3}}{\sin \frac{2\pi }{21}+\sin \frac{\pi }{3}}$

$=\frac{-1(\sin \frac{2\pi }{21}+\sin \frac{\pi }{3})}{\sin \frac{2\pi }{21}+\sin \frac{\pi }{3}}$

$=-1$