Report the Auth method for me2me connections.

remoting/webapp/base/js/client_session.js

Index: remoting/webapp/base/js/client_session.js
diff --git a/remoting/webapp/base/js/client_session.js b/remoting/webapp/base/js/client_session.js
index ac74e948708b8fafb0dede7b2edd3b0a97cb7ce9..ebb0bb49d822e0af978c7ddbde4122c019efbfb3 100644
--- a/remoting/webapp/base/js/client_session.js
+++ b/remoting/webapp/base/js/client_session.js
@@ -550,6 +550,7 @@ remoting.ClientSession.prototype.setState_ = function(newState) {
     this.connectedDisposables_ = null;
   }
 
+  this.logAuthMethod_();
   this.notifyStateChanges_(oldState, this.state_);
   // Record state count in an UMA enumerated histogram.
   recordState(this.state_);
@@ -557,6 +558,19 @@ remoting.ClientSession.prototype.setState_ = function(newState) {
       this.state_, this.error_, this.xmppErrorCache_.getFirstError());
 };
 
+/** @private */
+remoting.ClientSession.prototype.logAuthMethod_ = function() {
+  // The AuthMethod is undefined before the AUTHENTICATED stage for a
+  // successful connection or the FAILED stage for a failed connection.
+  if (this.state_ == remoting.ClientSession.State.AUTHENTICATED ||
+      this.state_ == remoting.ClientSession.State.FAILED) {
+    var authMethod = this.credentialsProvider_.getAuthMethod();
+    if (authMethod != null) {
+      this.logger_.setAuthMethod(authMethod);
+    }
+  }
+};
+
 /**
  * Records a Chromoting Connection State, stored in an UMA enumerated histogram.
  * @param {remoting.ClientSession.State} state State identifier.