The problem is to prove that: \(\displaystyle{\int_{{-\pi}}^{{\pi}}}{\int_{{-\pi}}^{{\pi}}}{\left({a}{\sin{{\left({x}\right)}}}+{b}{\cos{{\left({x}\right)}}}+{c}{\sin{{\left({y}\right)}}}+{d}{\cos{{\left({y}\right)}}}\right)}{e}^{{-{2}{\cos{{\left({y}-{x}\right)}}}+{a}{\cos{{\left({x}\right)}}}-{b}{\sin{{\left({x}\right)}}}+{c}{\cos{{\left({y}\right)}}}-{d}{\sin{{\left({y}\right)}}}}}{\left.{d}{x}\right.}{\left.{d}{y}\right.}\) I have

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