Sum of all values of $ x $ in $ [0,2 \pi] $ for which $ \sin x+\sin 2 x+\sin 3 x+\sin 4 x=0 $, is equal to: [JEE Main 2021, 25 Jul (Shift 1)]

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Sum of all values of \( x \) in \( [0,2 \pi] \) for which \( \sin x+\sin 2 x+\sin 3 x+\sin 4 x=0 \), is equal to: [JEE M…