Trigression!

Geometry Level 4

If

\({2\sin(2x)}\), \({\sin(4x)}\) and \({2\sin(6x)}\)

are in Arithmetic Progression, then for what values of \(x\), the above situation holds true. Select the correct option(s).

A: For all real values of \(x\).

B: For \(x\) is an integer multiple of \(\frac{\pi}{4}\).

C: For \(x\) is an integer multiple of \(\frac{\pi}{6}\).

D: For \(x\) is an integer multiple of \(\frac{\pi}{2}\).

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