The trace method for cotangent sums

This paper presents a combinatorial study of sums integer powers the cotangent. Our main tool is realization cotangent values as eigenvalues simple self-adjoint matrix with complex entries. We use trace method to draw conclusions about and series expansions generating function provide explicit evaluations; it remarkable that throughout calculations combinatorics are governed by higher tangent arctangent numbers exclusively. Finally, we indicate new approximation Riemann zeta at even arguments.