True/false quiz at the end of chapter 14 ofCalculus with Analytic Geometryby Purcell and Varberg, #25 reads,

If we restrict $$\rho, \theta, \phi$$ by $$\rho \ge 0, 0 \le \theta < 2\pi, 0 \le \phi \le \pi$$ then each point in three-space has a unique set of spherical coordinates.

I answered false because theta can take any value in [0, 2pi) for any point with phi equal to 0 or pi. Additionally, the origin (rho = 0) allows the same range for theta and also for phi to take any value in [0, pi].

The answer key has true for this statement.