What is the range of theta in Spherical Coordinate System?

Though theta is an angle, it can take value only up to 180^{o} and not 360^{o}. The reason is quite obvious. It is the minimum angle between the position vector of the point (r) and +Z axis.

Consider any point P present in the space. The position vector of this point i.e. r forms two angles with +Z axis, based on the nature of tracing, as shown in following figures. But, according to the definition, you should go with the minimum one as shown in figure.

So, for any point around the Z axis, the angle made by the r with +Z axis is **always less or equal to 180 ^{o} .**