The Latin phrase 'sine qua non' literally translates to 'without which, not.' In English usage, it refers to an essential action, condition, or ingredient that is absolutely necessary for something to exist or be achieved. Therefore, it describes an indispensable condition.

The Latin term 'via media' translates literally to 'middle way'. In a broader context, it refers to a moderate course of action or a compromise that exists between two opposing extremes. It is often used to describe a balanced approach to decision-making or philosophy.

The term 'fait accompli' is a French loan phrase that translates literally to 'an accomplished fact' or 'a thing already done'. It refers to a situation that has already happened and is therefore irreversible.

The term 'magnum opus' is derived from Latin, translating directly to 'great work.' It is most commonly used to describe the most significant or celebrated achievement of an artist, writer, or composer throughout their career. The provided explanation contained a contradiction regarding the option letter, which has been noted.

The Latin phrase 'ipse dixit' literally translates to 'he himself said it'. In modern usage, it refers to an assertion made without proof or support, relying solely on the authority of the person making the claim. It is often used to describe a dogmatic or unsupported statement.

A corrigendum is a formal term derived from Latin, specifically used in publishing and academic writing to refer to a list of errors discovered in a document after it has been printed, which must be corrected for accuracy.

The Latin term 'persona grata' translates literally to 'a pleasing person' or 'an acceptable person.' In diplomatic contexts, it refers to a foreign diplomat who is officially welcomed and accepted by the host government, as opposed to 'persona non grata,' which refers to an individual who is unwelcome or prohibited from entering a country.

The Latin term 'modus operandi' translates literally to 'method of operating.' It is commonly used in professional and forensic contexts to describe a particular way or method of doing something.

The Latin phrase 'Inter se' translates to 'among themselves' or 'between themselves'. It is frequently used in legal and formal contexts to describe an arrangement or relationship that exists exclusively between the parties involved, rather than with outside entities. It denotes a mutual or reciprocal interaction.

The term 'mala fide' is derived from Latin, meaning 'in bad faith'. It is used to describe actions taken with dishonest intent or deceitful motives. Therefore, 'treacherously' is the most appropriate synonym among the provided choices, as it captures the essence of acting with bad faith or betrayal.