A number of browsers now have an icon within tabs that show when a page is loading. At what point is it acceptable to prefer to use the icon in the tab to display loading information rather than a landing page or your own icon on a page?
Your question is vague but as per my understanding, you are asking about when to rely on the browsers page loading icon & when to add our own in the site
In most cases, browser's loading icon only appears till the time it hasn't loaded all the assets(js/css/etc) that are required by your page. And since those assets are not loaded, you might not be able to show the in page "Loading icon or modal"
Now there are many single page applications & ajax powered web apps out there which will refresh the content after the page is full loaded. In that case, the browser is not aware of the additional content that needs to be loaded in your page. Hence, the browser tab loading icon wont appear in such case & you require in page loading icon.
Browser tab loading icon & in page loading icon are used for entirely separate purposes. The former one indicates that the page is not completely loaded(resources required) whereas the latter one is used to indicate that the page & its immediate resources are loaded completely, but the additional data/new/refreshed content is getting loaded via async request.
I hope I made that clear