If a1,a2, and a3 are the three values of...

If `a_1,a_2, and a_3` are the three values of a which satisfy the equation `int_0^(pi/2)(sinx+acosx)^3dx-(4a)/(pi-2)int_0^(pi/2)xcosxdx=2` then find the value of `1000(a_1^2+a_2^2+a_3^2).`

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