Opening External Login Page

Hi all, I have an app running on Google App Engine, which provides endpoints for GET/POST requests (and a DB). It also comes with built-in authentication via Google accounts. I would like to open up a login page from within Unity in order to get the user's unique ID after signing in. I would like Unity to wait until sign-in completes before continuing. Is there a way to achieve this?

I have tried using the WWW class to make GET/POST requests, but they only seem to wait until the page/data loads, not necessarily waiting until the user has completed some task in the browser (i.e. signing into their Google account). I'm wondering if there is come clever way to achieve what I'm looking for... Thanks for any help!