einstimmig
unanimous
With no opposing vote or objection; with the agreement of everyone involved.
Der Vorstand hat den Beschluss einstimmig gefasst.
The board passed the resolution unanimously.

unanimous / monophonic
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unanimous
With no opposing vote or objection; with the agreement of everyone involved.
Der Vorstand hat den Beschluss einstimmig gefasst.
The board passed the resolution unanimously.

The word is made up of 'ein' (one), 'Stimme' (voice/vote), and the ending '-ig'. It literally means 'with one voice'. Both meanings are derived from this: a shared opinion (everyone has one voice) or a single melody (one musical voice).
Die Entscheidung für das neue Projekt war einstimmig.
The decision in favor of the new project was unanimous.
This meaning is often combined with nouns that express a decision or election. Typical phrases are 'ein einstimmiger Beschluss' (a unanimous resolution), 'eine einstimmige Entscheidung' (a unanimous decision), or 'eine einstimmige Wahl' (a unanimous election).
Der Kandidat wurde einstimmig zum neuen Vorsitzenden gewählt.
The candidate was unanimously elected as the new chairperson.
You can easily tell which meaning is intended from the context. If it is about politics, clubs, or group decisions, 'ungeteilt' (undivided/unanimous) is meant. If it is about music, especially early music or singing, 'mit nur einer Melodie' (with only one melody) is meant.
Der Ausschuss hat den Vorschlag einstimmig angenommen.
The committee unanimously accepted the proposal.
agreed / united
'Einig' and 'einstimmig' both have to do with shared agreement. 'Einig' generally says that people have the same opinion or reach a shared solution. 'Einstimmig' is used especially for votes or decisions when everyone is in favor and no one votes against it. Learners may confuse the words because both sound like full agreement. 'Einig' fits in many conversations; 'einstimmig' fits more precisely with an official resolution or election.

Der Verein hat den neuen Vorstand einstimmig gewählt.
The association unanimously elected the new board.
Nach dem Gespräch ist Timo sich mit seiner Lerngruppe über den Plan einig.
After the conversation, Timo agrees with his study group on the plan.