Move InspectorTask handling from MainThreadTaskRunner to Document

third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp

Index: third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp
diff --git a/third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp b/third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp
index 7f6f81b1b9e1f8e90603e49de0dae8c32a3632d1..01d79fb3a867d8e1868a11eed24e9bf5c4219662 100644
--- a/third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp
+++ b/third_party/WebKit/Source/web/ServiceWorkerGlobalScopeProxy.cpp
@@ -353,10 +353,14 @@ void ServiceWorkerGlobalScopeProxy::reportConsoleMessage(
 void ServiceWorkerGlobalScopeProxy::postMessageToPageInspector(
     const String& message) {
   DCHECK(m_embeddedWorker);
-  document().postInspectorTask(
-      BLINK_FROM_HERE,
-      createCrossThreadTask(&WebEmbeddedWorkerImpl::postMessageToPageInspector,
-                            crossThreadUnretained(m_embeddedWorker), message));
+  // The TaskType of Inspector tasks need to be Unthrottled because they need to
+  // run even on a suspended page.
+  getParentFrameTaskRunners()
+      ->get(TaskType::Unthrottled)
+      ->postTask(
+          BLINK_FROM_HERE,
+          crossThreadBind(&WebEmbeddedWorkerImpl::postMessageToPageInspector,
+                          crossThreadUnretained(m_embeddedWorker), message));
 }
 
 ParentFrameTaskRunners*