The number of solutions of the equation \) is:

The equation |sin x| = |cos 3x| is equivalent to sin^2 x = cos^2 3x, leading to sin x = ±cos 3x. Using identities, we derive four families of solutions: x = π/8 + kπ/2, x = 3π/8 + kπ/2, x = -π/4 + nπ, and x = π/4 + nπ. Counting distinct solutions in [-2π, 2π] yields 8 from each of the first two families and 4 from each of the last two, total 24, with no overlaps.