Three turns are always enough to point any object in any direction
Leonhard Euler showed that any orientation of a rigid body, however twisted, can be reached with just three rotations about coordinate axes. His three angles remain a standard way to describe orientation in physics and engineering, though twelve different axis orders mean everyone must say which convention they use.
Euler, the Swiss mathematician who lived from 1707 to 1783, defined the angles geometrically. Picture a fixed set of axes, x, y and z, and a second set, X, Y and Z, glued to a moving body. The line where the two horizontal planes cross is called the line of nodes. The first angle measures how far that line sits from the fixed x axis, the second measures the tilt between the two vertical axes, and the third measures how far the body's own X axis has turned from the line of nodes. The angles only make sense if both frames share the same handedness.
You can also build the same result from a sequence of turns. In intrinsic rotations each turn happens about the body's own axes, which move after every step. In extrinsic rotations each turn uses the fixed, motionless axes. A classic example is z-x-z: spin about the vertical, tip about a horizontal axis, then spin about the vertical again. Applying the extrinsic version means taking the angles in reverse order, a detail that trips people up.
Counting all the orders, there are twelve possible sequences. Six repeat the first axis at the end, such as z-x-z, and are known as proper or classic Euler angles. The other six use three different axes, such as x-y-z, and are called Tait–Bryan angles after Peter Guthrie Tait and George H. Bryan, who adapted the scheme for aeronautics and engineering. Those go by more familiar names too: heading, elevation and bank, or yaw, pitch and roll. Classic angles treat zero tilt as vertical, while the aviation versions treat zero as horizontal.
Because authors pick different axes, names and signs, any discussion of Euler angles should begin by defining them. Most use a right-hand rule for signs, and the middle angle spans only half a turn while the other two span a full circle.
Source: Euler angles
