diff --git a/youtube_dl/extractor/udemy.py b/youtube_dl/extractor/udemy.py
index 79c45f80e0..105826e9bb 100644
--- a/youtube_dl/extractor/udemy.py
+++ b/youtube_dl/extractor/udemy.py
@@ -122,7 +122,9 @@ def _handle_error(self, response):
             raise ExtractorError(error_str, expected=True)
 
     def _download_webpage_handle(self, *args, **kwargs):
-        kwargs.setdefault('headers', {})['User-Agent'] = 'Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_5) AppleWebKit/603.2.4 (KHTML, like Gecko) Version/10.1.1 Safari/603.2.4'
+        headers = kwargs.get('headers', {}).copy()
+        headers['User-Agent'] = 'Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_5) AppleWebKit/603.2.4 (KHTML, like Gecko) Version/10.1.1 Safari/603.2.4'
+        kwargs['headers'] = headers
         return super(UdemyIE, self)._download_webpage_handle(
             *args, **compat_kwargs(kwargs))