This equation came up when I was looking at the Fibonacci sequence; I adore its symmetry:
$$x^2 \cdot \sin \left(\frac{2\pi}{x-1} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x} \right) \right) = (x-1)^2 \cdot \sin \left(\frac{2\pi}{x} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x-1} \right) \right)$$
Question. The largest solution is ~3.1392. Is there an closed-form expression for this number?
