What is the locus of a surface when theta(θ) coordinate is constant in Spherical coordinate system?

There are three conditions of theta(θ)which are discussed below.

1. The locus of θ = constant for less than will form a conical curved surface above the XY plane with apex at origin and slant side making angle θ with + Z axis.

2. The locus of θ greater than will form a conical curved surface below the XY plane with apex at origin and slant side making angle θ with +Z axis.

3. The locus of θ equal to is exactly same as the XY plane.