The best way to approach a girl that you are in the same class with but have never talked to is to start a conversation with her about a topic that has to do with the class.
This is a very easy conversation opener.
Being that it relates to the both of you, it will be easier to have a brief conversation around a topic like this.
Since you both study in an amphitheater, it may be best to approach her before the class actually starts.
It is also best to make this approach somewhere around the entrance of the amphitheater.
This way, you don’t end up having to look all over the amphitheater as you try to ascertain where she is sitting.
When you approach her around the entrance of the amphitheater, just introduce yourself and proceed to ask her about something that was taught in class the last time around.
Tell her that you and your friends have been trying to make sense of what the professor meant when he said X during the last lecture.
Tell her that you are trying to get the opinion of other class members about it.
This is a great opener.
You are using something that the both of you have in common, thereby putting her at ease.
If the conversation flows well, it could lead to better conversations in the future and an opportunity for romance, if she also likes you.