Manco Inca hoped to use the disagreement between Almagro and Pizarro to his advantage and attempted the recapture of Cuzco starting in Feb. 1536. The siege of Cuzco was waged until the following spring, and during that time Manco's armies managed to wipe out four relief columns sent from Lima, but was ultimately unsuccessful in its goal of routing the Spaniards from the city. The Inca leadership did not have the full support of all its subject peoples and furthermore, the degrading state of Inca morale coupled with the superior Spanish siege weapons soon made Manco Inca realize his hope of recapturing Cuzco was failing. Manco Inca eventually withdrew to Tambo.:239-247 After the Spanish regained control of Cuzco, Manco Inca and his armies retreated to the fortress at Ollantaytambo where he, for a time, successfully launched attacks against Pizarro based at Cuzco and even managed to defeat the Spanish in an open battle.:247-249 When it became clear that defeat was imminent, Manco Inca retreated further to the mountainous region:259 of Vilcabamba and established the small Neo-Inca State, where Manco Inca and his successors continued to hold some power for several more decades. His son, Túpac Amaru, was the last Inca. After deadly confrontations, he was murdered by the Spanish in 1572. In total, the conquest took about forty years to complete. Many Inca attempts to regain the empire had occurred, but none had been successful. Thus the Spanish conquest was achieved through relentless force, and deception, aided by factors like smallpox and a great communication and cultural divide. The Spaniards destroyed much of the Incan culture and introduced the Spanish culture to the native population.

Based on the above article, answer a question. How many years passed between the siege of Cuzco and the murder of Tupak Amaru?
36