You clearly do not understand Spherical Polar Coordinates. The thing that makes it 3D is that the third component is Radius, which in your context is a constant, 1.
Assume a Cartesian (X-Y-Z) coordinate system oriented using the usual Right Hand Rule convention (make the XY plane horizontal, with X "forward", Y "to the left", and Z "up", so that if you curl your right hand fingers as though moving the X axis into the Y axis, your thumb points to the Z axis. Consider a point on the surface of the unit sphere (this takes only 2 coordinates, as we've "frozen" the radius). Project it onto the XY plane and onto the Z axis. What you call Theta is the angle that the component projected onto the XY plane makes with the X axis, and what you call Phi is the angle it makes with the +Z axis (actually, you don't have to define it this way, but this is the "usual" definition).
An easy way to see how these angles arise is to consider what you need to do to place the +Z axis on an arbitrary point on the surface of a sphere. Let's pretend it's a Globe, and describe this point by "Latitude" (a circle parallel to the equator) and "Longitude" (great circles that pass through both poles). Let's begin by rotating about the Y axis (using the right-hand rule, so a small rotation will yield a +X component) until our Latitude is correct. Now rotate about the Z axis until you are at the right longitude.
Rotations about the X-Y-Z coordinate axes are simple matrix transformations, and a Y rotation followed by a Z rotation is a simple matrix multiplication. Just Do the Math, it's really very simple.
BS
