Use Mikeal's Request library, you need to enable cookies support like this:
var request = request.defaults({jar: true})
So you first should create a username on that site (manually) and pass the username and the password as params when making the POST request to that site. After that the server will respond with a cookie which Request will remember, so you will be able to access the pages that require you to be logged into that site.
Note: this approach doesn't work if something like reCaptcha is used on the login page.
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