What is the Independence Day that Inoue Marina has been tweeting about lately?
独立記念日 (Dokuritsu Kinenbi, Independence Anniversary*) is a live reading event produced by 砂岡事務所プロデュース (Sunaoka Creative Artist Agency, official website (Japanese)).

A short introduction on "what is a live reading?", it's a live staged reading event where voice actors and actresses read a story script live in front of audiences, or to put it simply, live audio drama. Live Read is one of such internationally-acclaimed events that can be found on Wikipedia.

Back to Dokuritsu Kinenbi, it's a 2-day live reading event which took places on Saturday and Sunday. There were 5 scripts: 2 scripts on the first day and 3 scripts on the second day. Each script consisted of 4 casts and took around 75~80 minutes without breaks. As it could be inferred from the tweet, it has been produced 2 times (as of Feb 2018):


Dokuritsu Kinenbi: 12-13 Aug 2017 (official site (Japanese))
Dokuritsu Kinenbi vol.2: 3-4 Feb 2018 (official site (Japanese))


This is how the stage for vol.2 looks like



From Sunaoka Jimusho's official Twitter account



*The English name is taken from these Facebook posts: Ishikawa Kaito and Hanae Natsuki