Export a private webstore API to call into the new inline sign-in flow.

chrome/common/extensions/api/webstore_private.json

Index: chrome/common/extensions/api/webstore_private.json
diff --git a/chrome/common/extensions/api/webstore_private.json b/chrome/common/extensions/api/webstore_private.json
index f80ff335a23e978ebebc00a3e49ac60e043a2be2..6f08fbfe63dde30e5152a18f6a696e5efd79521b 100644
--- a/chrome/common/extensions/api/webstore_private.json
+++ b/chrome/common/extensions/api/webstore_private.json
@@ -252,6 +252,24 @@
             ]
           }
         ]
+      },
+      {
+        "name": "signIn",
+        "description": "Signs the user into Chrome.",
+        "parameters": [
+          {
+            "name": "continue_url",
+            "type": "string",
+            "description": "The continue URL to navigate to once sign-in completes."
+          },
+          {
+            "name": "callback",
+            "type": "function",
+            "description": "Called if the sign-in method was invoked incorrectly (e.g. with an invalid continue URL), sign-in is unavailable (e.g. in Incognito), or if the user is already signed in. Upon such a failure, chrome.runtime.lastError will be set to 'invalid_continue_url', 'signin_is_disallowed', 'signin_failed', or 'user_is_already_signed_in'.",
+            "optional": true,
+            "parameters": []
+          }
+        ]
       }
     ]
   }