There exists a triangle \( A B C \) satisfying....
There exists a triangle \( A B C \) satisfying
(1) \( \tan A+\tan B+\tan C=0 \)
\( \mathrm{P} \)
(2) \( \frac{\sin A}{2}=\frac{\sin B}{3}=\frac{\sin C}{7} \)
(3) \( (a+b)^{2}=c^{2}+a b \) and \( \sqrt{2}(\sin A+\cos A)=\sqrt{3} \)
(4) \( \sin A+\sin B=\frac{\sqrt{3}+1}{2}, \cos A \cos B=\frac{\sqrt{3}}{4}=\sin A \) \( \sin B \)
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