How to connect to rainwater downpipe

I've got a lean-to roof around 2 m high and want to fit guttering to it. There's a rainwater pipe nearby. What is the proper way to connect to it?

Would it be a tee connection like this?
The downpipe below it would need a spigot at the top then, which means replacing it?

In any case, my downpipe is square and made of aluminium and I couldn't find the equivalent tee fitting for it.

I've seen hoppers being used but it would look odd to have a hopper 1m from the ground!

Get an aluminium branch in square.
There are a few companies online selling alloy products.

Or get one made

OK, just found it. But looks like I still need a spigot on the downpipe for connection...