Entire functions on two nonparallel lines belongs to $L^2(-\infty,\infty)$

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Suppose that $f$ is an entire function of exponential type. If its restriction on two nonparallel lines belongs to $L^2(-\infty,\infty)$, show that $f=0$. I am sorry that I don't how to write the first line of a proof. Can anyone give me some advice? Thanks!