The answer seems obvious, unless I have not understood your question correctly: 

The triangle wave E(theta)=-1+2 |theta|/2 is said to be the best local realistic approximation to the quantum singlet state correlation function, in the sense that for this wave the original Bell inequality |E(theta1)-E(theta2)|

Dear Prof. David Gill,

                                     Unlike my previous person who has given an algebraic solution using Bell's Theorem I am going to give you an answer using String Theory in a Relativistic Setting resulting in Geometric Fractal factorisation using Theorems developed in my String Theory and Econophysics problem of Coal Mining paper and the String theory of Stock Markets paper on my RG page. You will notice that I have derived the result that a Hexagonal "Beehive" Geometry is more efficient String Theoretically than a spherical geometry when it comes to relativistic factorisation of a particle system econophysically (genetically) with money-utility (Von Neumann) implicit conversion and hence the "Econophysics Haag's theorem" developed by me in another published paper on the RG page. Now the most physically efficient (entropy maximising) factorisation of a hexagonal geometry under D_Branes String integration is the hub and spike Archimedian factorisation topology (time diffeotopy) which gives the periodic triangle wave by geometric triangulation and genetic algorithmic linearisation. Please refer to my Classification and Systems Integration theorem in my Information Structure paper. I hope that gives a solution. Thanks for asking. SKM QC