Really need an explanation of how 0.999 repeating is = to 1. Very confused

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

There are 3232 forwards and 8080 guards in leo's basketball league. leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards. if leo creates the greatest number of teams possible, how many guards will be on each team?

Solve for x where 0 equation: cot^2x+2cotx+1=0