Is the fast valid, and is a make-up day obligatory for one who broke her fast, thinking that the muezzin had called the Maghrib prayer, then discovered that she had broken her fast a quarter or a third of an hour before the adhan?

Scholars have differed regarding one who eats or drinks, thinking that the sun has set or that night still remains, and then it becomes clear that the opposite is true: is he required to make up that fast or not? The majority of scholars hold that making up the fast is obligatory. However, the Zahiriyyah and Shaykh al-Islam Ibn Taymiyyah are of the view that making it up is not obligatory, citing the verse: "Our Lord, do not impose blame upon us if we forget or make a mistake." (Quran 2:286). It has been reported that Umar ibn al-Khattab, may Allah be pleased with him, had two opinions on this matter: at one time, he indicated that making up the fast was not necessary, and at another, he indicated its ease. Ibn al-Qayyim held that analogical deduction (qiyas (definition)) necessitates the dropping of the make-up fast, and that the ignorant person who makes a mistake is more deserving of excuse than one who forgets. The opinion that making up the fast is not obligatory is sound in terms of evidence. Nevertheless, the safer and more blameless course of action is to make up that day.