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Is this (the phrase/word ごとが) a grammar point or vocabulary? I tried to look
it up in Takoboto dictionary but it doesn't return a specific word.

Also, if the phrase/word 「ごとが」 is a grammar point. How do I use it?

The context, where I found the word, lies in the song 翼をください ([an ending song
version of
Nichijou](http://nichijou.wikia.com/wiki/Tsubasa_wo_Kudasai#Japanese))
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question
particle-が parsing
What does「ごとが」mean?
I'm assuming you mean the ごとが in

> いま私の願いごとがかなうならば翼がほしい

If this is the case, then you're parsing the sentence incorrectly. The ごと
forms part of a noun phrase with 願い. You can find it on [Takeboto under
お願い事](http://takoboto.jp/?w=1949390). Here's the underlying structure (I've
used bold to highlight the different grammatical components):

> **願いごと** が **かなう**

The が is your standard subject marker. Thus, the subject of the sentence is
願いごと and the main verb is かなう, which means for a 願い to be come true/be
fulfilled.
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answer
Presumably you are referring to this part of the lyrics:

> いま わたしの願い **ごとが**  
>  叶うならば 翼が欲しい  
>  この 背中に鳥のように  
>  白い翼 つけてください

In which case you are parsing it incorrectly. It actually breaks down like
this

> いま わたしの 願いごと が

Where 願いごと means "desire" or "thing wished for". In conjunction with the next
line, it's saying "If my wish were fulfilled now..."
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answer