How to type 《 》and 〈〉efficiently on Mac OS X?

Solution 1: using Emacs

If you have an Emacs window open almost all the time like I do, you can use Emacs to do it, on macOS or other OSs. Specifically, Ctrl-x, Enter, then start typing the character's name, namely, "LEFT DOUBLE ANGLE BRACKET". As you finish typing more and more letters, type Tab to prompt a list of matching characters, until it auto-completes it to the unique one.

Solution 2: using Chinese input method

These characters are CJK book quotation marks. Many Chinese input methods map < to 〈 and Shift+< to 《, respectively. So, if you install a Chinese input method, switch to Chinese mode, and type < or Shift+<, you will get 〈 and 《. To type the normal English keyboard <, just switch the input method back to English.

For « and »

OPTION + \
OPTION + SHIFT + \

For ‹ and ›

OPTION + SHIFT + 3
OPTION + SHIFT + 4

I'm writing from the year 2021, using macOS 11.1 on an American English keyboard.

This is the same content as a 2018 answer, with better markup.