Regroup terms.
\[2D\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}+\sin{(\frac{7{\pi }^{c}}{26})}+\sin{(\frac{3{\pi }^{c}}{26})}=0\]
Subtract \(\sin{(\frac{7{\pi }^{c}}{26})}\) from both sides.
\[2D\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}+\sin{(\frac{3{\pi }^{c}}{26})}=-\sin{(\frac{7{\pi }^{c}}{26})}\]
Subtract \(\sin{(\frac{3{\pi }^{c}}{26})}\) from both sides.
\[2D\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}=-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}\]
Divide both sides by \(2\).
\[D\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}=\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2}\]
Divide both sides by \(\sin{(\frac{11{\pi }^{c}}{26})}\).
\[D\sin{(\frac{31{\pi }^{c}}{26})}=\frac{\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2}}{\sin{(\frac{11{\pi }^{c}}{26})}}\]
Simplify \(\frac{\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2}}{\sin{(\frac{11{\pi }^{c}}{26})}}\) to \(\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}}\).
\[D\sin{(\frac{31{\pi }^{c}}{26})}=\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}}\]
Divide both sides by \(\sin{(\frac{31{\pi }^{c}}{26})}\).
\[D=\frac{\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}}}{\sin{(\frac{31{\pi }^{c}}{26})}}\]
Simplify \(\frac{\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}}}{\sin{(\frac{31{\pi }^{c}}{26})}}\) to \(\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}}\).
\[D=\frac{-\sin{(\frac{7{\pi }^{c}}{26})}-\sin{(\frac{3{\pi }^{c}}{26})}}{2\sin{(\frac{11{\pi }^{c}}{26})}\sin{(\frac{31{\pi }^{c}}{26})}}\]
D=(-sin((7*PI^c)/26)-sin((3*PI^c)/26))/(2*sin((11*PI^c)/26)*sin((31*PI^c)/26))
