How did Joiada establish Joas as king and remove Athalia?

In the seventh year of Queen Athalia's reign, Joiada the high priest took courage and summoned five captains of hundreds: Azarias son of Jeroham, Ismahel son of Johanan, Azarias son of Obed, Maasias son of Adaias, and Elisaphat son of Zechri, entering into a formal covenant with them. These commanders journeyed throughout Juda, assembling the Levites from all the cities of Juda alongside the patriarchal heads of Israel's households, and brought them to Jerusalem. The entire assembly made a covenant with the young king in the house of God, as Joiada declared to them that the king's son must reign according to the Lord's promise regarding the house of David.

Joiada then established the tactical plan for the operation. He instructed that a third part of the priests, Levites, and porters coming in for the Sabbath watch should guard the gates, a third part should secure the king's house, and a third part should be stationed at the Foundation Gate, while the remainder of the people stayed in the courts of the Lord's house. To protect sacred holiness, only the consecrated priests and ministering Levites were permitted to enter the temple interior. Joiada issued an explicit, coercive order that the Levites must surround the king with weapons in hand, commanding that if any unauthorized person entered the temple, he must be slain, and that the guards must stay with the king both in his coming in and going out. The Levites and all Juda complied with Joiada's orders, retaining the men who came in for the Sabbath duty alongside those who had completed their rotation and were scheduled to depart, for the high priest did not permit the outgoing companies to leave. Joiada distributed to the captains the spears, shields, and targets that King David had dedicated in the house of the Lord, posting armed men with swords drawn from the right side of the temple to the left, before the altar and the sanctuary, encircling the king.

They brought out the king's son, placed the crown upon him along with the testimony, giving him the law to hold in his hand, and Joiada the high priest and his sons anointed him, praying and acclaiming, "God save the king." Hearing the noise of the people running and praising the monarch, Athalia entered into the temple of the Lord. Beholding the boy king elevated upon the entrance step, surrounded by military commanders and royal units while the populace celebrated, sounded trumpets, played diverse instruments, and shouted praises, she tore her garments and cried out, "Treason, treason!"

Joiada the high priest went out to the army captains and commanded them to take her forth outside the precinct of the temple, ordering that she be killed with the sword once outside, for the priest commanded that she should not be slain in the house of the Lord. The soldiers seized her by the neck, and when she reached the horse gate of the palace, they put her to death there. Joiada then made a covenant between himself, the king, and all the people, pledging that they should be the people of the Lord. The assembly proceeded to the house of Baal and destroyed it, breaking down its altars and idols, and slaying Mathan the priest of Baal before the altars. Joiada instituted supervisory offices within the Lord's house, committing their oversight to the priests and Levites whom David had distributed throughout the temple to offer holocausts with joyful singing in accordance with the law of Moses, placing porters at the gates so that no unclean person could enter. Finally, the commanders, valiant men, and nobles escorted King Joas down from the house of the Lord through the upper gate into the royal palace, placing him upon the throne of the kingdom. The entire populace of the land celebrated with great joy, and Jerusalem rested in tranquil peace once Athalia had been put to death by the sword.