\( \frac{\sin 770^{\circ}}{\cos 65^{\circ}-\sin 205^{\circ}} \)

Step 1 ：\( \frac{\sin (360^{\circ} \times 2 + 50^{\circ})}{\cos 65^{\circ} - \sin (180^{\circ} + 25^{\circ})} \)

Step 2 ：\( \frac{\sin 50^{\circ}}{\cos 65^{\circ} - (- \cos 25^{\circ})} \)

Step 3 ：\( -\frac{\sqrt{6} - \sqrt{2}}{4} \)