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Sum of coefficients in a shifted cubic expansion

High school · ●●○○○ 20 pts

If the equation 1+x+x2+x3=a0+a1(1−x)+a2(1−x)2+a3(1−x)31+x+x^{2}+x^{3}=a_{0}+a_{1}(1-x)+a_{2}(1-x)^{2}+a_{3}(1-x)^{3} holds for all real xx, where a0a_{0}, a1a_{1}, a2a_{2}, a3a_{3} are real constants, find the value of a1+a2+a3a_{1}+a_{2}+a_{3}.

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