[i]This post is subject to change with future updates.[/i]
The Three of coins is a shiny piece of garbage, except for one distinct & useful place.
[b]What is it?: [/b] It's a coin that boosts your chances to receive an exotic from "sources in the world" for 4 hours, purchased for 31 legendary shards from Xur.
[b]Does it work?: [/b] By all player accounts currently, no - except for one area.
[b] Where [i]Does[/i] it work?: [/b] Cashing in luminous milestones players have reported the coin giving them 2 or even 3 exotics at a time from each milestone. This does not happen every time, nor is it guarantee that you'll even get a single exotic. However, this is one notable area where the coin has been deemed to [i]potentially[/i] be doing it's job.
[b]How to apply it effectively: [/b] Until an update on the coin happens, you should complete every milestone for that week - then pop a coin & cash em' in for potentially higher chances on exotics.
Good luck & happy hunting!
Perhaps luminous/powerful engrams have a higher percentage chance of getting an exotic which is further added upon with the Three of Coins. I myself have been reasonably lucky getting numerous exotic rolls from Heroic events planet side (EDZ mainly as that appears to have a really decent event turnover).
A majority of the time I do agree in that it feels like it does nothing but when put into perspective that the percentage or flat bonus it grants (we won't know until this is stipulated) when combined with the already low percentage you have in getting an exotic engram anyway that does make sense.