How to add a forms authentication cookie to the request

A common problem is how to add an forms authentication cookie to the request.
The solution is to add the forms authentication cookie when performing a HttpWebRequest.

Uri uri = new Uri("http://services.mysite.com/document/documentservice.svc");

HttpWebRequest webRequest = (HttpWebRequest)WebRequest.Create(uri);       

HttpCookie cookie = HttpContext.Current.Request.Cookies[FormsAuthentication.FormsCookieName];

Cookie authenticationCookie = new Cookie(FormsAuthentication.FormsCookieName, cookie.Value, cookie.Path, HttpContext.Current.Request.Url.Authority);

webRequest.CookieContainer = new CookieContainer();

webRequest.CookieContainer.Add(authenticationCookie);

WebResponse myResponse = webRequest.GetResponse();

Stream stream = myResponse.GetResponseStream();