- We examine the size of a real trigonometric polynomial of degree at most n having at least zeros in K := (mod 27) (counting multiplicities). This result is then used to give a new proof of a theorem of Littlewood concerning flatness of unimodular trigonometric polynomials. Our proof is shorter and simpler than Littlewood's. Moreover our constant is explicit in contrast to Littlewood's approach, which is indirect. 2000 Copyright retained by the authors.