[Media Router] Add UMA metrics for Media Router Dialog WebUI performance.

chrome/browser/media/router/media_router_metrics.h

Index: chrome/browser/media/router/media_router_metrics.h
diff --git a/chrome/browser/media/router/media_router_metrics.h b/chrome/browser/media/router/media_router_metrics.h
index fddfd45884c5ead60a46990ce5a1e1a8219bc4d4..0db8bd0c00b8a7d21f60ebe0d636e033e85c2565 100644
--- a/chrome/browser/media/router/media_router_metrics.h
+++ b/chrome/browser/media/router/media_router_metrics.h
@@ -5,6 +5,8 @@
 #ifndef CHROME_BROWSER_MEDIA_ROUTER_MEDIA_ROUTER_METRICS_H_
 #define CHROME_BROWSER_MEDIA_ROUTER_MEDIA_ROUTER_METRICS_H_
 
+#include "base/time/time.h"
+
 namespace media_router {
 
 // NOTE: Do not renumber enums as that would confuse interpretation of
@@ -52,6 +54,16 @@ class MediaRouterMetrics {
   // Records why the media route provider extension was woken up.
   static void RecordMediaRouteProviderWakeReason(
       MediaRouteProviderWakeReason reason);
+
+  // Records the duration it takes for the Media Router dialog to open and
+  // finish painting after a user clicks to open the dialog.
+  static void RecordMediaRouterDialogPaint(
+      const base::TimeDelta delta);
+
+  // Records the duration it takes for the Media Router dialog to load its
+  // initial data after a user clicks to open the dialog.
+  static void RecordMediaRouterDialogLoaded(
+      const base::TimeDelta delta);
 };
 
 }  // namespace media_router