Starting from the Riesz-Fejer lemma and its generalizations, especially from the fact that any degree \(n\) trigonometric polynomial on the unit circle is the square of the modulus of an outer polynomial of degree \(n\), fails to generalize to more variables, the paper analyses the case when a trigonometric polynomial of several variables that is non-negative on the \(d\)-torus can be approximated with a single modulus square. To do this, for a trigonometric polynomial written as sums of squares, the outer component is defined. It is shown that the outer component is unique and may be determined by a two-step procedure based on semidefinite programs. Using Schur complements, some specific properties can be proved for the outer component. Based on some numerical experiments, some conjectures on trigonometric polynomials with zero outer components are given.