On the approximation of entire functions by trigonometric polynomials

Let a set $B$ have the following properties: if $z\in B$, then $z\pm2\pi\in B$ and the intersection of $B$ and the strip $0\le\operatorname{Re}x\le\pi$ is a closed and bounded set.
In this paper we study the approximation of a continuous on $B$ and $2\pi$-periodic function $f(z)$ by trigonometric polynomials $T_n(z)$. We establish the necessary and sufficient conditions for the function $f(z)$ to be entire and specify a formula for calculating its order. In addition, we describe some metric properties of periodic sets in a plane.