My English teacher told me that "going to go" doesn't exist in English but I saw it many times. For example "The whole band is going to go to show their support". I'd like to know if it's possible to use it or not.
Yes, it's fine, providing you want it to mean what it says.
Going to... indicates a future action:
So you can express the future action of going somewhere:
You can add the reason for that future action.
Yes, you can use "going to" before a verb when you already knew in advance that you'd be doing that. For instance, "I'm going to tell this to my English teacher".
And Go is not an exception. You can perfectly well say "I'm going to go home tomorrow".
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