general

if we move 90 degree in a flat syuface four times and simalarlly we can reach the same point.
if we move same 4 seps in a round surface ball we will attain the starting point or not. if it s possible send the derived equation.

You need to do your own homework.

That said, simple tracing out paths with your finger on a ball will show that four right angles do not necessarily form a closed path on a sphere. It can, but that depends on how long each of the segments are. There is a case where exactly three right angles will bring you back to the starting point, for example. It's not so hard to find if you think about it.

As for the exact equations, this is your homework so definitely your job.