>>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, 0 – π/4, π – π/4}]

s has two local minimums
and one local maximum
in this interval:
–1 < θ/(π/4) < 3