Calculate: sin (2 arc tan 3).

The given expression is sin (2 arc tan 3).
\(=\sin \left(2 \tan ^{-1} 3\right) \operatorname{\ if\ tan}^{-1} 3=0 \\ \Rightarrow \tan \theta=3 \\ =\sin (2 \theta) \\ =\frac{2 \tan \theta}{1+\tan ^{2} \theta}\\=\frac{2 \times 3}{1+9}\\=\frac{6}{10}\\=\frac{3}{5}\)

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