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In the year 2013 . . .

-- The moon is not at Third Quarter on April 21.

At 0000Z on 21 Apr, it's a waxing gibbous, about 74% illuminated.

Its Right Ascension is then 09h 57m .

-- The last Third Quarter before April 21 occurs on April 3 at 0500Z.

RA is then 18h 57m .

-- The next Third Quarter after April 21 occurs on May 2 at 1300Z.

RA is then 20h 53m .

(Times and RAs are rounded, which, I'm guessing, will be close enough for your purposes.)

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