fix check of is_otel_instrumented (#1313)

CHANGELOG.md

@@ -21,6 +21,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   ([#1208](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/1208))
 - `opentelemetry-instrumentation-aiohttp-client` Fix producing additional spans with each newly created ClientSession
 - ([#1246](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/1246))
+- Add _is_openetlemetry_instrumented check in _InstrumentedFastAPI class
+  ([#1313](https://github.com/open-telemetry/opentelemetry-python-contrib/pull/1313))
 
 ## [1.12.0-0.33b0](https://github.com/open-telemetry/opentelemetry-python/releases/tag/v1.12.0-0.33b0) - 2022-08-08
 

instrumentation/opentelemetry-instrumentation-fastapi/src/opentelemetry/instrumentation/fastapi/__init__.py

@@ -247,6 +247,7 @@ def __init__(self, *args, **kwargs):
             client_response_hook=_InstrumentedFastAPI._client_response_hook,
             tracer_provider=_InstrumentedFastAPI._tracer_provider,
         )
+        self._is_instrumented_by_opentelemetry = True
 
 
 def _get_route_details(scope):

instrumentation/opentelemetry-instrumentation-fastapi/tests/test_fastapi_instrumentation.py

@@ -274,6 +274,14 @@ def test_request(self):
             self.assertEqual(span.resource.attributes["key1"], "value1")
             self.assertEqual(span.resource.attributes["key2"], "value2")
 
+    def test_mulitple_way_instrumentation(self):
+        self._instrumentor.instrument_app(self._app)
+        count = 0
+        for middleware in self._app.user_middleware:
+            if middleware.cls is OpenTelemetryMiddleware:
+                count += 1
+        self.assertEqual(count, 1)
+
     def tearDown(self):
         self._instrumentor.uninstrument()
         super().tearDown()