Sines everywhere 2

Geometry Level 4

\[\large \sin(x)-2\sin(2x)-\sin(3x)=2\sqrt{2}\]

Find the sum of all real \(x\in [0;2\pi]\) satisfying the equation above, submit your answer to 2 decimal places.

Note: If you think there is no root, submit 100.00 as your answer.

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