A new kind of P´al type (0; 0; 1) interpolation

Consider the trignometric polynomials $ r_{n}(x)=frac{cos (2n+1)frac{theta }{2}}{cos frac{theta }{2}}$ and $s_{n}(x)=frac{sin (2n+1)frac{theta }{2}}{sin frac{theta }{2}}.$ These polynomials are such that their zeros are interscaled and neither of the polynomials is the extrema of the other polynomial. On these interscaled set of nodes we study an interpolation process when Lagrange data is prescribed on one set of nodes and Hermite data is prescribed on the other set of nodes.