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If \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) are the angles of a triangle and \( \tan \mathrm{A}=1, \tan \mathrm{B}=2 \), prove that \( \tan \mathrm{C}=3 \). If \( a \), \( b, c \) are the corresponding sides, then prove that \( \frac{a}{\sqrt{5}}=\frac{b}{2 \sqrt{2}}=\frac{c}{3} \).
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