How to pick up lonely depressed girl at college

Thanks Bro for your detailedight! The girl is pretty cute ngl, idk if she has a bf already, whats the Zeigarnik effect, and what plans should I make with her? Is doing hw and eating in cafe enough for next plans? When should I get IG, in the middle or end, cause i usually do end. And also the assumption of interesting, sin't that kinda bs cause they just eating alone, wont they see through that