Trigonometry of a tetrahedron the role of "O" yields four such identities, but at most three of them are independent; if the "clockwise" sides of three of the four identities are multiplied and the product is inferred to be equal to the product of the "counterclockwise" sides of the same three identities, and then common factors are cancelled from both sides, the result is the fourth identity. Three angles are the angles of some triangle if and only if their sum is 180° (π radians). What condition on 12 angles is necessary and sufficient for them to be the 12 angles of some tetrahedron?
Euler angles reached as follows: In sum, the three elemental rotations occur about "z", "x" and "z". Indeed, this sequence is often denoted "z-x-z" (or 3-1-3). Sets of rotation axes associated with both proper Euler angles and Tait–Bryan angles are commonly named using this notation (see above for details). There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same. The six possible sequences are: Angles are commonly defined according to the right-hand rule. Namely, they have positive values when they represent a rotation that appears clockwise