particle が - What are the grammar rules behind this clause, 「才能があ ろうがなかろうが」?

才能があろうがなかろうが、そんなもん他人が決める事じゃない。どこの部に所属するかなんぞ俺が決める事だ

I'm asking about the bolded clause. This is casual dialogue, in case there's any confusion about that.

I don't normally put Japanese through Google Translate, but I did so here and the clause was translated to "Whether there is talent or not,"... Why is that? I'd love to know the grammar rules behind this. Thanks in advance.

Answer

According to 明鏡国語辞典, the が is a conjunctive particle (接続助詞), and it expresses 逆接の仮定条件 (contradictory hypothetical condition? "even if~"/"no matter~~") when attached to the volitional auxiliaries 「う・よう」「まい」.

Examples:

• 人が何と言おうが、私はやる。（言おうと(も)）
  No matter what others may say, I'll do it.


• 私がどこに行こうが、君には関係ない。 (行こうと(も))
  No matter where I go, it's not your concern.


• どこにいようと(も)、いつもあなたを想っています。
  No matter where I might be, I'll always be thinking of you.
  _{～と and ～が have the same meaning and are interchangeable in most situations, but ～が can sound a bit stronger and is more often used for sentences with a negative or decisive nuance, eg 「あなたには関係ない」「私の勝手だ」「絶対～～する」.}

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「volitional form A (～う/よう) + が/と + volitional form B (～う/よう) + が/と 」

This is a fixed construction for saying "(Regardless of) Whether A or B" (「たとえAしたとしてもBしたとしても」 in a less literary way).

In this formula you use two different verbs/adjectives, which are ある and ない in your example. 「あろう」 and 「なかろう」 are the volitional forms of 「ある」 and 「ない」, respectively.

「才能があろうがなかろうが」 here in your example literally means "(Regardless of) Whether there is talent or there isn't", i.e., "Whether I have talent or not." ＝「才能があろうとなかろうと」.

Examples:

• 結婚しようが、一人でいようが、私の勝手でしょ。(結婚しようと一人でいようと)
  Whether I get married or stay single, it's none of your business.


• 雨が降ろうが風が吹こうが、私は行く。(雨が降ろうと風が吹こうと)
  Whether it rains or blows, I'll go.

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You could also rephrase your example as 「才能があろうがあるまいが」「才能があろうとあるまいと」, repeating the same verb 「ある」:

「volitional form (～う/よう) + が/と + negative volitional (～まい) + が/と」

You use this structure to mean "(Regardless of) Whether ~~ or not" (「～ても～なくても」 or 「たとえ～たとしても～なかったとしても」 in a less literary way).

In this formula you repeat the same verb, first time in the affirmative volitional form (～う・よう) and the second the negative volitional form (～まい).

Examples:

• 君が気に入ろうが気に入るまいが、これが僕のやり方だ。(気に入ろうと気に入るまいと)
  Whether you like it or not, this is the way I do it.


• 信じようが信じまいが、これは真実なのだ。(信じようと信じまいと)
  
  It's true, whether you believe it or not.