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Algebra Level 4

If \(a\) and \(b\) are real numbers satisfying \[\sqrt{\sin^2a+2\sin b+4}-\sqrt{\sin^2a+2\sin a+3}\]\[=\sqrt{\sin^2a+\sin a+3\sin b+2}-\sqrt{\sin^2a+\sin a-\sin b+5},\] find the value of \(\sin a+\sin b\).

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