Change WokerThread to use a blink::WebThread.

Source/core/inspector/WorkerRuntimeAgent.cpp

Index: Source/core/inspector/WorkerRuntimeAgent.cpp
diff --git a/Source/core/inspector/WorkerRuntimeAgent.cpp b/Source/core/inspector/WorkerRuntimeAgent.cpp
index 65f72d93ca710136490d7ddd166fadfd8baf704c..5978eeb340ecaf7a72e605800f43f43636df6b42 100644
--- a/Source/core/inspector/WorkerRuntimeAgent.cpp
+++ b/Source/core/inspector/WorkerRuntimeAgent.cpp
@@ -37,7 +37,6 @@
 #include "core/inspector/InstrumentingAgents.h"
 #include "core/inspector/WorkerDebuggerAgent.h"
 #include "core/workers/WorkerGlobalScope.h"
-#include "core/workers/WorkerRunLoop.h"
 #include "core/workers/WorkerThread.h"
 
 namespace blink {
@@ -106,10 +105,12 @@ void WorkerRuntimeAgent::willEvaluateWorkerScript(WorkerGlobalScope* context, in
 
     m_paused = true;
     MessageQueueWaitResult result;
+    context->thread()->willEnterNestedLoop();
     do {
-        result = context->thread()->runLoop().runDebuggerTask();
+        result = context->thread()->runDebuggerTask();
     // Keep waiting until execution is resumed.
     } while (result == MessageQueueMessageReceived && m_paused);
+    context->thread()->didLeaveNestedLoop();
 }
 
 } // namespace blink