Summation formulae for finite tangent and secant sums

In a series of papers [6], [7], [8], [9] and [10] it has been shown that nine remarkably general families of the finite trigonometric sums could be summed in closed form by making use of the calculus of residues and choosing a particularly convenient integration contour. In this sequel, new summation formulae for three general families of finite tangent and secant sums have been deduced by the same approach.