A bullet of mass m and initial velocity v₀ passes through a block of mass M suspended by an unstretchable, massless string of length L from an overhead support. It emerges from the collision on the far side traveling at v₁ < v₀. This happens extremely quickly (before the block has time to swing up) and the mass of the block is unchanged by the passage of the bullet (the mass removed making the hole is negligible, in other words). After the collision, the block swings up to a maximum angle θ_max and then stops. Find θ_max.