A point \( O \) is the centre of a circle circumscribed about a tri...

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A point \( O \) is the centre of a circle circumscribed about a triangle \( A B C \). Then \( \overrightarrow{O A} \sin 2 A+\overrightarrow{O B} \sin 2 B \)
P \( +\overrightarrow{O C} \sin 2 C \) is equal to
(1) \( (\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}) \sin 2 A \)
(2) \( 3 \overrightarrow{O G} \), where \( G \) is the centroid of triangle \( A B C \)
(3) \( \overrightarrow{0} \)
(4) none of these
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