Final answer:
Whether King Arthur consents to Sir Agravain's plan is dependent on the specific text and the version of the Arthurian legend being referred to, but traditionally, King Arthur does not give initial consent in classic tales.
Step-by-step explanation:
The question pertains to the legend of King Arthur, Sir Lancelot, and Guenevere which is a core element of English literature and medieval folklore. If we consider the canonical stories of the Arthurian legend, there is no definitive version that states King Arthur consents to Sir Agravain’s plan to trap Lancelot and Guenevere. The stories of Arthurian legend have been told and retold through various texts, and different adaptations might have different takes on this event. It is essential to refer to a specific text to answer this question accurately. However, in many classic tales, Agravain and Mordred are the ones who plot against Lancelot and Guenevere, usually without Arthur's initial consent.