In this article some results on the value distribution theory of analyticfunctions defined in angles of \(\mathbb{C}\) , due mainly to B. Ja. Levin and A. Pfluger,will be extended to the more general situation where the functions are defined inangles of \(\mathbb{C}\backslash\{ 0\}\) . More precisely, angles \(S ( \theta_{1},\theta_{2}) \) with vertex at the origin will beconsidered and where a singularity at zero is allowed. An special class of thesefunctions are those of completely regular growth for which it is proved a basic resultwhich yields an expression of the density of its zeros in terms of the indicatorfunction.
