The word "embroiler" means to involve someone in a complicated situation or problem. Synonyms for this word can be "entangle", "complicate", "implicate", "involve", "embarrass", "enmesh", "embroil", or "mire". These words all convey the same idea of pulling someone into a complex or troublesome scenario. Other related words could include "trouble", "confuse", "obfuscate", "confound", "bewilder", or "perplex". Remember, when using synonyms, it is important to ensure that they convey the exact meaning you intend, and to use them appropriately within the context of your writing.