If your app URL is NOT in a zone that allows scripting access to the system, you won't be able to make this change.
mysite.com <- is in the restricted zone
the browser does not allow scripting to make these kind of changes so it won't be able to add itself to the Trusted zone.
This is a security feature. If a site could do this then the whole zone thing would be useless as a hacker's script would be able to add itself to a trusted zone, which would increase it's security access to the browser, and work from there.
If you figure out a way around this, please let me know. I'd be curious to see how it's done.