Actually, the word "vain" is not in the original Greek. The verse should simply say not to use repetitious prayer. (I teach Greek, so you can trust me.

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In the first place, my Baptist church is traditional, avoiding CCM. So we don't use the "7-11" pop music type of singing: 7 words 11 times. We certainly don't sing that CCM song. We sing traditional hymns which are not repetitious.
Secondly, the verse does not say "worship" but "pray." So you are off target. Singing is not the same as praying, though sometimes a hymn can have a prayer in it.