Q:

Direct access call for a twig template from a twig template gives 404

I'm trying to call for a Twig template _template from a Twig template, particularly from within AngularJS <script type="text/javascript"></scirpt> tags. A console log says, that the file was not found on the server with status of 404. Using {% include '' %} or {% embed '' %}interferes with AngularJS somehow. Does any way around exists to access that Twig template, without breaching the security?
Troubleshooting part of js:
$mdDialog.show({
  templateUrl: '_template',
})

A:

Not sure exactly what you trying to do here?  Call a Twig template from Angular?
Twig is a server side technology, Angular is getting parsed on the client side. The only way Craft is going to parse a Twig template is when it encounters a URL. 
Instead of calling the Twig template directly, you call the URL, which could match a template. Inside templates, make a folder like angular-views and then inside that put a file called md-dialog.twig.  From the front end, now you can call it from Angular like http://example.com/angular-views/md-dialog (the .twig is optional).
If you're trying to use Angular inside of a Twig template, you may want to use something like {% verbatim %} and then put your JS/Angular templating between those tags to make sure Twig doesn't touch any of it. 

