Add a box on the Analytics page which allows you to enter your GTM Container ID and then automagically insert the two GTM Container code snippets in the appropriate places.
Google Tag Manager container code now has two code snippets.
The first code snippet needs to go as high as possible in the <head>.
The second code snippet needs to go immediately after the <body> tag. The only way I know to do this at the moment is with a custom embed.