Trigonometry! #58

Geometry Level 4

3sin2x+2cos2x+31sin2x+2sin2x=283^{\sin 2x + 2\cos^{2} x}+3^{1-\sin 2x+2\sin^{2}x}=28

Find the number of solutions to the above equation if 0x2π 0 \leq x \leq 2\pi.

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