My iphone is saying I don't have enough storage to download pitch perfect?

I have an itunes gift card to buy Pitch Perfect for rent on the itunes store and when I went in to buy it it said I didn't have enough storage. Therefore I deleted photos and apps to buy the movie. When I came back to buy it again it said I still didn't have enough storage. This is after deleting over 800 pictures and almost 15 applications. It is now only saying I have 3 GB remaining and saying I have used 10.5 GB.
The only apps I have are below:
Photos & Camera -3.6 GB used
Music - 575 MB
Instagram - 115 MB
YouTube - 34.6 MB
PINK Nation - 34.1 MB
We Heart It - 29.5 MB
Etsy - 27.6 MB
Find Iphone - 19.2 MB
Video - No Data
And when I got to purchase Pitch Perfect it says: "Can't Download: There's not enough storage to download "Pitch Perfect". You can manage your local device storage usage in Settings.
All I want is to rent this movie. If anyone could help me that would be absoultely fantastic.

Yes same thing happened to me. You have to delete some stuff.than buy it again it takes about 5 hours to download! >_< SUCKS!

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