Registration on the game server through social nets (FB, VK)

Hi, guys!
There is a server for game, there is a client on Unity. Communication with the server through sockets.
How to make registration on the server by means of Facebook or Vkontakte?
For the usual sites as I understood, the scheme such:
1. The client pressing by the Enter through Facebook button,
2. the site gives out a special reference on which the browser passes and gets on a social network form.
3. The client enters the login the password,
4. the social net requests permissions to a profile for this site (appendix).
5. If it is successful, the user is thrown on the REDIRECT_URL page which was specified in application controls in a social net.
6. Along with it CODE on which the server of the site receives a token by means of which gets access to the user data from a social net is transferred to REDIRECT_URL from a form of a social net.
7. Further the server looks if the client isn't registered in base - registers.

How to turn the same scheme on the client of Unity? Unity have no built-in WebView as it is admissible, in XCode.
Or the scheme another can? Or I am not right in this scheme at all?

 

Really nobody knows? Well though something....