Problem

Problem

Find the number of solutions for, sin⁡5θ⋅cos⁡3θ=sin⁡9θ⋅cos⁡7θ in [0,π2].\sin 5\theta \cdot \cos 3\theta = \sin 9\theta \cdot \cos 7\theta \text{ in } \left[ 0, \frac{\pi}{2} \right].

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