The Ecthesis (Greek: Ἔκθεσις) is a letter published in 638 CE by the Byzantine emperor Heraclius which defined monotheletism as the official imperial form of Christianity.
Consequently, the emperors at Constantinople were always seeking some method of rapprochement to heal the breach in the church, and thereby prevent the empire's enemies from taking advantage of the internal divisions.
With the reign of Heraclius, he and the Patriarch Sergius had attempted to find common ground between the Chalcedonians and the Non-Chalcedonians by issuing the doctrine of the single energy of Christ during the mid 630s.
A copy was posted in the narthex of Hagia Sophia, and when Sergius died in December 638, it looked as if Heraclius might actually achieve his goal, with the eastern patriarchs agreeing to the formula, and gaining many adherents across the east, including Cyrus of Alexandria and Arkadios II of Cyprus.
His successor Pope John IV also rejected the doctrine completely, leading to a major schism between the eastern and western halves of the orthodox church.
The new conquerors allowed the Non-Chalcedonians to practice their faith in peace, which suited them since they no longer had the need to bend their beliefs to the Byzantine hierarchy (but they still had to provide the jizya).