Mathematical principle of planar Z-plasty

To extend the work of precursors attempting to use Z-plasties with angles that have arbitrary degrees and may or may not be equal in size, a comprehensive study was done to clarify and simplify the correlation among the angles, limbs, and diagonals of the geometrical construction of Z-plasties. In geometry, the truth of a proposition must be proved; it is a question to which the answer must be found. By law and formula, a ternary trigonometric equation was derived from a simplified geometric diagram by a trigonometric approach. A procedure declaration accompanies this formula; neither was previously mentioned in the literature.