Here is how to add a Shairport Sync device to the Apple Home application on iOS 15.3.1. Note that Shairport Sync has to be built with AirPlay 2 support.

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Step 0: Speaker & TV access.
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In the Home app > Home settings "Allow Speaker & TV access", select the option "Anyone On the Same Network".

Step 1: Open the "Home" app
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Tap the `Add Accessory` panel or choose "Add Accessory" from the `+` symbol in the top right:

![IMG_3678](https://user-images.githubusercontent.com/4265913/157615721-e42a07e3-f93e-49d0-9233-e7b92a577459.jpg)

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Step 2: "More options..."
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Step 2: Tap `More options...`

![IMG_3679](https://user-images.githubusercontent.com/4265913/157616118-79c6d494-ce6e-4666-a6de-53cb40d0e751.jpg)


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Step 3: Select your Shairport Sync device:
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Your Shairport Sync device should appear here, though you may have to scroll. Tap the appropriate icon and follow the remaining instructions.

![IMG_3680](https://user-images.githubusercontent.com/4265913/157616475-22ee2eb6-56f4-4368-a1ed-d925f9984f1e.jpg)