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Sine of a double angle from a shifted sine

High school · ●●○○○ 20 pts

Given α∈(0,π2)\alpha \in (0, \frac{\pi}{2}) and sin⁡(2α−π3)=33\sin (2\alpha - \frac{\pi}{3}) = \frac{\sqrt{3}}{3}, find sin⁡2α\sin 2\alpha. Round to four decimal places.

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angle sum identityPythagorean identitytrigonometric equationsquadrant analysis