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TrigonometryHardTrigonometric Equations

Trigonometric Equations · Hard problem

Find the sum of all solutions of sin⁡(x+π3)+sin⁡(x−π3)=sin⁡2x\sin\left(x + \dfrac{\pi}{3}\right) + \sin\left(x - \dfrac{\pi}{3}\right) = \sin 2x in the interval [0,2π)[0, 2\pi).