Why does the New World Translation 'add' the words, within square brackets, "the angel of" at Zechariah 3:2?

All Bible translations add words to make the intended meaning of the original language clear to the readers of another language. Some Bibles indicate the added words in footnotes. Some, like the King James Version, frequently signifies these additions by italicizing such added words. The New World Translation usually indicates added words with brackets [ ].

In the case of Zechariah 3:2, the New World Translation is not the only Bible to add "the angel of" or its equivalent here.

A New Commentary on Holy Scripture explains their reason why:

"[v]2. the Lord. Read the angel of the Lord, as the speech that follows seems to require."- SPCK, London, reprint 1946 (1st pub.1928).

Another footnote, this one belonging to The Revised English Bible (1989) reveals why it reads at Zechariah 3:2 "The angel said to Satan." The footnote states: "3:2 angel: prob[able] r[ea]d[in]g, so Syriac; Heb[rew] LORD." (Additions in square brackets aim to aid in better understanding.)

This is similiar to what we can read in the footnote to this verse in the Reference Edition of the New World Translation (1984): "2* "The angel (messenger) of Jehovah," Sy[riac]; MLXXVg, "Jehovah."
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Other translations that render this passage the same way as the New World Translation:

"The angel of the Lord said to Satan," (Good News Translation)

"The angel of Yahweh said to Satan," (The Jerusalem Bible; Scroll down)
"And the angel of the LORD..." (New American Bible)

"The LORD rebuke you," the Angel of the LORD said..." (The Holy Bible, An American Translation; W.F. Beck)
"The messenger of Yahweh..." (vs.1) (The Emphasised Bible; J. B. Rotherham)
"Then [the messenger] of Jehovah..." (2001 Translation – An American English Bible)

"So the angel of the LORD said...." (The Bible, An American Translation; Powis-Smith and Goodspeed)