Tilting a Cylindrical Oil Pot

An oil pot has a body shaped as a cylinder (wall thickness negligible) with base diameter $6.4\text{ cm}$ and height $16\text{ cm}$, and it contains oil to a height of $12.1\text{ cm}$. Its spout has length $13.4\text{ cm}$ (volume negligible), makes a $30^{\circ}$ angle with the body, and the base of the spout is at height $3\text{ cm}$ above the bottom of the pot. The pot is slowly tilted about one edge of its base. Find the smallest tilt angle (in degrees, to the nearest $0.01^{\circ}$) at which the oil just begins to flow out of the spout.