Sines everywhere

Geometry Level 5

\[\large \sin\bigg(\frac{3 \pi}{10}-\frac{x}{2}\bigg)=\frac{1}{2} \sin\bigg(\frac{\pi}{10}+\frac{3x}{2}\bigg)\] How many real values of \(x\in[-\pi;\pi]\) satisfy the equation above?

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