The intervention of Denmark, Sweden and Poland-Lithuania into Livonia began a period of struggle for control of the Baltic, known contemporaneously as the dominium maris baltici. While the initial war years were characterised by intensive fighting, a period of low-intensity warfare began in 1562 and lasted until 1570 when fighting once more intensified. Denmark, Sweden and to some extent Poland-Lithuania were occupied with the Nordic Seven Years' War  taking place in the Western Baltic, but Livonia remained strategically important. In 1562, Denmark and Russia concluded the Treaty of Mozhaysk, respecting each other's claims in Livonia and maintaining amicable relations. In 1564, Sweden and Russia concluded a seven-years truce. Both Ivan IV and Eric XIV showed signs of mental disorder, with Ivan IV turning against part of the Tsardom's nobility and people with the oprichina that began in 1565, leaving Russia in a state of political chaos and civil war.
Question: Why did Denmark, Sweden and Poland-Lithuania intervene?
Answer: Livonia remained strategically important