[Media Router] Add UMA metrics to record the load time for route controls

chrome/browser/resources/media_router/elements/route_details/route_details.html

 <link rel="import" href="chrome://resources/html/polymer.html">
 <link rel="import" href="chrome://resources/html/i18n_behavior.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-button/paper-button.html">
 <link rel="import" href="extension_view_wrapper/extension_view_wrapper.html">
 <link rel="import" href="../route_controls/route_controls.html">
 <dom-module id="route-details">
   <link rel="import" type="css" href="../../media_router_common.css">
   <link rel="import" type="css" href="route_details.css">
   <template>
     <div id="route-information"
         hidden$="[[!shouldShowRouteInfoOnly_(controllerType_)]]">
       <span>[[activityStatus_]]</span>
     </div>
     <template is="dom-if" if="[[!useWebUiRouteControls]]">
       <extension-view-wrapper id="extension-view-wrapper" route="[[route]]"
+          route-details-open-time="[[openTime_]]"
           is-extension-view-ready="{{isExtensionViewReady}}"
           hidden$="[[!shouldShowExtensionView_(controllerType_)]]">
       </extension-view-wrapper>
     </template>
     <template is="dom-if" if="[[shouldShowWebUiControls_(controllerType_)]]">
-      <route-controls id="route-controls"></route-controls>
+      <route-controls id="route-controls"
+          route-details-open-time="[[openTime_]]"></route-controls>
     </template>
     <div id="route-action-buttons" class="layout">
       <paper-button flat class="route-button button"
           id="start-casting-to-route-button"
           hidden$="[[computeCastButtonHidden_(route, changeRouteSourceAvailable_)]]"
           on-tap="startCastingToRoute_">
         <span>[[i18n('startCastingButtonText')]]</span>
       </paper-button>
       <paper-button flat class="route-button button"
           id="close-route-button"
           on-tap="closeRoute_">
         <span>[[i18n('stopCastingButtonText')]]</span>
       </paper-button>
     <div>
   </template>
 <script src="route_details.js"></script>
 </dom-module>