If \( \mathrm{a} \& \mathrm{~b} \) are real numbers between \( 0 \& 1 \) such that the points \(...

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If \( \mathrm{a} \& \mathrm{~b} \) are real numbers between \( 0 \& 1 \) such that the points \( \mathrm{z}_{1}=\mathrm{a}+\mathrm{i}, \mathrm{z}_{2}=1+ \) bi \&
PD \( \mathrm{z}_{3}=0 \) form an equilateral triangle, then find the values of \( a \) and \( b \) .
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