>>16807191
>s = (2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ))

Plot[(2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ)), {θ, π – π/4, 2*π – π/4}]

s has zero local minimums
and two local maximums
in this interval:
3 < θ/(π/4) < 7