Explicit Constant c(N, θ)

The constant $c(N,\theta)$ is given explicitly by $$c(N,\theta) = 2^{N-1} \cdot (-1)^N \cdot \prod_{k=0}^{N-1} \cos\!\left(\theta + \frac{2\pi k}{N}\right) - T_N(0).$$ This is the only $\theta$-dependent part of the relationship $S_N(x;\theta) = T_N(x) + c(N,\theta)$.