In order to access the internet through the Facebook Login asking for a Like, users have to follow these steps:
STEP 1
The user clicks on the Facebook Login button in the splash page.
STEP 2
The user logs into Facebook, if he is not already logged:

STEP 3
The user allows or disallows the application to get information from his Public profile and email address.
STEP 4
The user can click on "Like" or "skip and continue" button to access Internet, is NOT possible to force to "Like" the page.

NOTE
The "Skip and Continue" is part of the Facebook login procedure, as a mandatory option, accordingly to the official Facebook policy.
For more info click here.
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Facebook social actions overview