う・よう + が～まいが

When both the positive and negative volitional auxiliary verbs are combined with a verb in Japanese, it has the nuance of 'whether or not (A)', the result will be (B)'. This is quite emphatic, and has a literal meaning similar to 'say it does (A) or say it doesn't (A), it will still be (B)'.
As a reminder, the positive auxiliary verbs of volition are either う or よう, depending on what they are being connected to, while the negative auxiliary verb of volition is まい. Either the case marking particle が or と will appear after both the positive and the negative, with が being slightly more common.

• 忘年会(ぼうねんかい)に出席(しゅっせき)しようが出席(しゅっせき)するまいが、会費(かいひ)はみんなからもらっています。
  Whether you attend the year-end party or not, we will collect the admissions fee from everyone.
• 雨(あめ)が降(ふ)ろうが降(ふ)るまいが、明日(あした)は絶対(ぜったい)に釣(つ)りに行(い)くと決(き)めた。
  Whether it rains or not, I have decided to go fishing tomorrow.

While this structure is primarily seen after verbs, it is important to remember that other auxiliary verbs such as だ can be conjugated in the same way, as can い-Adjectives with the less common かろう structure. This means that both nouns, な-Adjectives and い-Adjectives can also appear using a similar grammar pattern. However, because the negative volitional まい cannot pair with these structures, an antonym will usually appear with them instead, with both words using the う or よう positive volitional.

• 楽(たの)しかろうが楽(たの)しくなかろうが、学校(がっこう)は子供(こども)の仕事(しごと)だから学校(がっこう)には行(い)かなくてはだめだ。
  Whether it is fun or not, school is a child's job, so you must go to school.
• 安全(あんぜん)だろうが安全(あんぜん)でなかろうが、２メートル以上(いじょう)の場所(ばしょ)に上(あ)がる場合(ばあい)は安全帯(あんぜんたい)を必(かなら)ず装着(そうちゃく)してください。
  Whether it is safe or not, always wear a safety belt when you climb to a place higher than 2 meters.
• 犬(いぬ)であろうが猫(ねこ)であろうが、どちらにしても動物(どうぶつ)なので軽(かる)い気持(きも)ちで買(か)っては行(い)けない。
  Whether it is a dog or a cat, they are both animals, so they must not be bought on a whim.

Based primarily on the use of volitionals, this grammar pattern will often indicate the speaker's strong will or opinion that will not change regardless of (A).