If I use Angle Shot to attach an equipment, do I have to pay the attach cost of that equipment if it has one?

No — Angle Shot attaches the equipment for free; you only pay Angle Shot's own cost (2 Energy, Fury, Reaction).

Angle Shot instructs the attach as a game action (Rule 435.2), and Attach is not the Equip ability — Equip is the activated ability that costs something (Rule 818.1.b). Since the card says "attach," no equip cost is involved (compare FAQ 2814 / 7575). Note the equipment must be controlled by the same player as the chosen unit, and you may instead choose to detach it — you must pick one of the two options.