Close TabPage From Within Itself

There is no such concept as "close" for a tab page. You can delete one, here is how:
http://msdn.microsoft.com/en-us/library/system.windows.forms.tabcontrol.tabpages.aspx[^],
http://msdn.microsoft.com/en-us/library/system.windows.forms.tabcontrol.tabpagecollection.aspx[^],
http://msdn.microsoft.com/en-us/library/system.windows.forms.tabcontrol.tabpagecollection.remove.aspx[^] or:
http://msdn.microsoft.com/en-us/library/system.windows.forms.tabcontrol.tabpagecollection.removeat.aspx[^].

Note, that there is no such thing as "from within itself" or not. Typically, you invoke some events, and the event handler is an anonymous method or a method of, typically, a form or a window. For example:

myDeleteButton.Click += (sender, eventArgs) => { // or menu item click, same thing...
    myTabControl.TabPages.RemoveAt(myTabControl.SelectedIndex);
    // if myDeleteButton is placed on some page, and you can click it, it means that the page is selected before the click
    // this button itself will be removed with the page, as the result of this action,
    // so what?
};

The references above are for System.Windows.Forms, but the code for WPF (and probably some other libraries) will be very similar.

Note: you should always tag the UI library or application type you are using when UI is involved.

—SA