Find all continuous and bounded functions $g$ with : $$\forall x \in \mathbb R, 4g(x)=g(x+1)+g(x-1)+g(x+\pi)+g(x-\pi).$$

I have posted this question, here, but no answer.

Find all continuous and bounded functions $g$ with : $$\forall x \in \mathbb R, 4g(x)=g(x+1)+g(x-1)+g(x+\pi)+g(x-\pi).$$

I have posted this question here, but received no answer.

Find all continuous and bounded functions $g$ with : $$\forall x \in \mathbb R, 4g(x)=g(x+1)+g(x-1)+g(x+\pi)+g(x-\pi)$$

I have posted this question, here, but no answer.

Find all continuous and bounded functions $g$ with : $$\forall x \in \mathbb R, 4g(x)=g(x+1)+g(x-1)+g(x+\pi)+g(x-\pi).$$

I have posted this question, here, but no answer.