If I use Angle Shot on an already attached equipment, do I have to detach it?

Yes, you must choose one of the two options provided by Angle Shot.

According to the card text, when you play Angle Shot, you must:

1. Attach that Equipment to that unit, OR
2. Detach that Equipment from that unit.

Because the card gives you a choice between two specific actions, you must perform one of them. If you choose to detach the equipment, it will be detached from the unit it is currently attached to.