Trying to work out when my girlfriend's period is discreetly

I hate to ask such a personal question and I don't want to generalise women's emotions but I want to help my girlfriend and she does seem to have certain patterns in mood. I wonder whether it has something to do with her period. In general she's very lively, upbeat, sharp, confident and outgoing despite her insecurities and quite conservative upbringing from a Hindu family. However every 4-5 weeks there's a change lasting around 2 weeks. During the first week her mood fluctuates a lot, most notably she is really horny/suggestive in a way she wouldn't think of at other times, and more spontaneous. Although there can be no sex before marriage, this is when we're most likely to be intimate and she'll be unashamedly passionate in her advances (most of the time she's reserved and just giggles or coos when we kiss or cuddle). The second week she has a complete U-turn in mood; she becomes depressed, very irritable, complains of being tired a lot and doesn't want to hang out with me. I try to keep conversation light and cheer her up/ask how she is Sometimes she'll just yell at me and blame me for random things, other times she won't respond to a text for 3 days, and sometimes she's able to have conversation but it's very sober and mild, any sexy talk goes out of the window. She will also ask some (often heated and sometimes concerning/stressful) questions about our relationship, what I think of her etc., insecurities really come to forefront all of a sudden. She's my first ever relationship that lasted more than a few weeks (and I'm her first full stop), so I've never dealt with this before. Also I'm not sure how to approach the subject considering it and the whole concept of relationships/sexuality seems to be quite sensitive for her. And of course trying to put all her feelings down to 'Time of the Month' is quite insensitive. How should I go about this?

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