Find the coefficient of \( \mathrm{x} \) in the expansion of \( \left|\begin{array}{lll}(1+x)^{2...

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Find the coefficient of \( \mathrm{x} \) in the expansion of \( \left|\begin{array}{lll}(1+x)^{22} & (1+x)^{44} & (1+x)^{66} \\ (1+x)^{33} & (1+x)^{66} & (1+x)^{99} \\ (1+x)^{44} & (1+x)^{88} & (1+x)^{144}\end{array}\right| \)
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