Which is the best and quickest way to share a large video file on WhatsApp?

Whatsapp doesn't allow files greater than 16 MB to be transferred. Are you sure your video is just 3.3 MB? That doesn't seem possible. It is a 30 minute video after all.
I'll tell you the best way to share bigger files through Whatsapp. Upload your heavier files on your Google drive and post the link of that file or folder to the person you want to share. There is a setting to let the link be public. Make sure you switch it on. Using that link the person can download your video or watch it online. Hope this helps.

There is one app known as WhatsTools which can be downloaded from the play store and can be used for sending the large files.

After installing it you have to run this app and it will give a menu item as 'Turn on Service'.
Click or tap it to start.
Now Select Settings -->Accessibility -->WhatsTools Service.
Toggle it to 'On'.
It will give option of Google Drive and will ask you to 'sign in' in Google Drive.
Now sign in with your Google account (If you do not have then make one Google account).
Click or tap on the + sign.
It will display type of files like audio, video etc. Select the type you want to send.
It will now display files. Select the file you want to send.
Now click or tap on the Share menu.
Select WhatsApp in the next menu.
Now Select the WhatsApp contact of the recipient you want to share the file with and tap on Send.
The file will be uploaded to Google Drive and a link will be send to the recipient.
The recipient will click the link and get the file downloaded to his mobile.

This method can also be used to send the file to other applications like Facebook, Hike, Gmail etc.

Since you are using android , please try following app to degrade little video quality and share. Video Compress, VidCompact, Video Dieter 2 are some of good apps. Else just search for video compress or video converter . You will have option to select quality level before compressing it. It is just like try it out method. Once which you like most keep and delete others.