Trigonometric Equation

The animation sweeps a ray around the unit circle to show that the angle $\theta = 3x + \pi/4$ completes 1.5 rotations, hitting the two target directions where $\cos(\theta) = -\sqrt{2}/2$ twice each for a total of four roots. It then maps these four intersection points back to the original $x$-axis, identifying the solutions as $x = \pi/6, \pi/3,