It is just a convention for $ 0 \le \theta \le \pi $. You can write it your way (indeed you can "include" a constant in a variable) but in that case $ 0 \le \theta \le \pi / 2 $.

It is just a convention for $ 0 \le \theta \le \pi $. You can write it your way (indeed you can "include" a constant in a variable) but in that case $ 0 \le \theta \le \pi / 2 $.

But we take this convention for unique coordinates. If you refer to the Spherical coordinate system

you can see that if you want a unique set of spherical coordinates for each point of the sphere, you need to restrict their range.

It is just a convention for $ 0 \le \theta \le \pi $. You can write it your way (indeed you can "include" a constant in a variable) but in that case $ 0 \le \theta \le 2\pi $.

It is just a convention for $ 0 \le \theta \le \pi $. You can write it your way (indeed you can "include" a constant in a variable) but in that case $ 0 \le \theta \le \pi / 2 $.