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So how would you open up to her in an open environment now that your mindset is correct
Confidently walk up to her, say "HI, my name is ___", shake her hand, have good eye contact. If you are looking for some special line that is going to open them, you shouldn't be. What you say to her may be situational, you may have just stopped and said she was cute. It does not really matter just show her that you are a fun, dominant male with the above mindset^. Don't use some line that you've been saving in your head all day to use, it will come off as fake and may not work with your given situation. Just go practice that is how you will find what will work best for you. Nobody can tell you exactly what to say, because there are different situations and everyone has different techniques that work better with themselves than it would with another PUA. Trial and error is your opportunity.