Use GoogleAuthUtil's getToken instead of AccountManager

sync/android/BUILD.gn

 # Copyright 2014 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 import("//build/config/android/config.gni")
 import("//build/config/android/rules.gni")
 
 android_library("sync_java") {
   deps = [
     "//base:base_java",
     "//net/android:net_java",
     "//third_party/cacheinvalidation:cacheinvalidation_javalib",
     "//third_party/cacheinvalidation:cacheinvalidation_proto_java",
     "//third_party/jsr-305:jsr_305_javalib",
     "//third_party/android_tools:android_gcm_java",
+    google_play_services_library,
   ]
   srcjar_deps = [ ":java_enums" ]
   DEPRECATED_java_in_dir = "java/src"
 }
 
 android_library("sync_javatests") {
   testonly = true
   deps = [
     ":sync_java",
     "//base:base_java",
@@ skipping 12 matching lines @@
     "//sync/internal_api/public/base/model_type.h",
   ]
 }
 
 generate_jni("jni_headers") {
   sources = [
     "java/src/org/chromium/sync/ModelTypeHelper.java",
   ]
   jni_package = "syncer"
 }