Find all the solutions of this equation x^2 - 3 [ ( x - 6 ) ] = 3

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Find all the solutions of this equation

x^2 - 3 \left[ \sin \left( x - \frac{\pi}{6} \right) \right] = 3, \text{ where } [\cdot] \text{ represents the greatest integer function.}