Add documentation for configuring a forward proxy. (#10443)

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diff --git a/docs/SUMMARY.md b/docs/SUMMARY.md
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--- a/docs/SUMMARY.md
+++ b/docs/SUMMARY.md
@@ -7,6 +7,7 @@
   - [Installation](setup/installation.md)
   - [Using Postgres](postgres.md)
   - [Configuring a Reverse Proxy](reverse_proxy.md)
+  - [Configuring a Forward/Outbound Proxy](setup/forward_proxy.md)
   - [Configuring a Turn Server](turn-howto.md)
   - [Delegation](delegate.md)
 
diff --git a/docs/setup/forward_proxy.md b/docs/setup/forward_proxy.md
new file mode 100644
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+# Using a forward proxy with Synapse
+
+You can use Synapse with a forward or outbound proxy. An example of when
+this is necessary is in corporate environments behind a DMZ (demilitarized zone).
+Synapse supports routing outbound HTTP(S) requests via a proxy. Only HTTP(S)
+proxy is supported, not SOCKS proxy or anything else.
+
+## Configure
+
+The `http_proxy`, `https_proxy`, `no_proxy` environment variables are used to
+specify proxy settings. The environment variable is not case sensitive.
+- `http_proxy`: Proxy server to use for HTTP requests.
+- `https_proxy`: Proxy server to use for HTTPS requests.
+- `no_proxy`: Comma-separated list of hosts, IP addresses, or IP ranges in CIDR
+  format which should not use the proxy. Synapse will directly connect to these hosts.
+
+The `http_proxy` and `https_proxy` environment variables have the form: `[scheme://][<username>:<password>@]<host>[:<port>]`
+- Supported schemes are `http://` and `https://`. The default scheme is `http://`
+  for compatibility reasons; it is recommended to set a scheme. If scheme is set
+  to `https://` the connection uses TLS between Synapse and the proxy.
+
+  **NOTE**: Synapse validates the certificates. If the certificate is not
+  valid, then the connection is dropped.
+- Default port if not given is `1080`.
+- Username and password are optional and will be used to authenticate against
+  the proxy.
+
+**Examples**
+- HTTP_PROXY=http://USERNAME:PASSWORD@10.0.1.1:8080/
+- HTTPS_PROXY=http://USERNAME:PASSWORD@proxy.example.com:8080/
+- NO_PROXY=master.hostname.example.com,10.1.0.0/16,172.30.0.0/16
+
+**NOTE**:
+Synapse does not apply the IP blacklist to connections through the proxy (since
+the DNS resolution is done by the proxy). It is expected that the proxy or firewall
+will apply blacklisting of IP addresses.
+
+## Connection types
+
+The proxy will be **used** for:
+
+- push
+- url previews
+- phone-home stats
+- recaptcha validation
+- CAS auth validation
+- OpenID Connect
+- Federation (checking public key revocation)
+
+It will **not be used** for:
+
+- Application Services
+- Identity servers
+- Outbound federation
+- In worker configurations
+  - connections between workers
+  - connections from workers to Redis
+- Fetching public keys of other servers
+- Downloading remote media
+
+## Troubleshooting
+
+If a proxy server is used with TLS (HTTPS) and no connections are established,
+it is most likely due to the proxy's certificates. To test this, the validation
+in Synapse can be deactivated.
+
+**NOTE**: This has an impact on security and is for testing purposes only!
+
+To deactivate the certificate validation, the following setting must be made in
+[homserver.yaml](../usage/configuration/homeserver_sample_config.md).
+
+```yaml
+use_insecure_ssl_client_just_for_testing_do_not_use: true
+```