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Open your instagram app and tap on the options icon of any video that you want to download.
When the option menu appears you have to tap on the 'copy share url' option from the menu.
An overlay dialog appears at the bottom of the screen promting you to download the video you have chosen. Tap on the download button.
A detail screen pops up on the bottom of the screen showing the download links. You can choose the resolution in which you want to download from here.
Once resolution is selected a dialog appears which allows you to change your download location and select number of network threads for fast downloading.
Tap on download button and your download begins. You can tap on the download icon on the top of the screen to view your downloads.