Should he repeat the words of the muezzin or pray Tahiyyat al-Masjid?

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It is better for workers to hasten to pray when they hear the adhaan
Ruling on praying Witr in the same way as Maghrib

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Related Answers:
Praying Taraaweeh in congregation in Ramadaan is Sunnah and not a bid’ah (innovation)
Is it Sunnah to separate one naafil prayer from another by moving to the first spot or to another spot?
What is it permissible to do of naafil prayers at times when prayer is makrooh?
It is better for workers to hasten to pray when they hear the adhaan
Ruling on praying Witr in the same way as Maghrib

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