yep, you are at fault, you are required to be able to stop without hitting the car in front of you at all times.

The fact that you weren't able to avoid hitting the car in front means you didn't actually maintain your distance, and you were at fault.

If you had dashcam footage you might have been able to share _some_ of the blame, if the other driver braked that hard without warning. as others have said, since you hit the car in front, you did not maintain enough distance, thus you still have some of the blame.

If he was an idiot for having to stop suddenly, doesn't that mean you are also? You did the same thing!

Hopefully, you won't have another car until you get some drivers ed, you fat tail-gater!

So, the person in front of you had a reason to stop... they had a person in front of them who they almost hit. So had you been paying attention to the entire situation, you would have seen the car in front and anticipated the necessity to stop. Had you ACTUALLY been maintaining your distance, no matter what the car in front of you did, you should have been able to stop... that or you needed new brakes... Either way, you're at fault. Don't tailgate

Best to maintain as much distance as possible, perhaps several car lengths more than what is recommended. Sure, some folks might get annoyed, but not nearly as annoyed as they would if they were in front of you and you hit them. Life goes on, be more careful next time.