Add desktop engagement metrics.

chrome/browser/ui/views/frame/browser_frame.cc

Index: chrome/browser/ui/views/frame/browser_frame.cc
diff --git a/chrome/browser/ui/views/frame/browser_frame.cc b/chrome/browser/ui/views/frame/browser_frame.cc
index 7eb9ff2e37afc14940222f6ccefe0fec5be75936..541cc221fcd36f4674770421fc142f8531c852be 100644
--- a/chrome/browser/ui/views/frame/browser_frame.cc
+++ b/chrome/browser/ui/views/frame/browser_frame.cc
@@ -219,6 +219,8 @@ void BrowserFrame::OnNativeWidgetActivationChanged(bool active) {
     // ourselves as the last active browser window to ensure that we get treated
     // as such by the rest of Chrome.
     BrowserList::SetLastActive(browser_view_->browser());
+  } else {
+    BrowserList::NotifyBrowserNoLongerActive(browser_view_->browser());
   }
   Widget::OnNativeWidgetActivationChanged(active);
 }