\(\displaystyle{\cos{{2}}}\theta={1}-{2}{{\sin}^{{2}}\theta}\)

\(\displaystyle\frac{{28}}{{53}}={1}-{2}{{\sin}^{{2}}\theta}\)

\(\displaystyle-\frac{{25}}{{53}}=-{2}{{\sin}^{{2}}\theta}\)

\(\displaystyle\frac{{25}}{{106}}={{\sin}^{{2}}\theta}\)

\(\displaystyle\sqrt{{\frac{{25}}{{106}}}}={\sin{\theta}}\)

\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\)

\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\times\frac{\sqrt{{106}}}{\sqrt{{106}}}\)

\(\displaystyle{\sin{\theta}}=\frac{{{5}\sqrt{{106}}}}{{106}}\)

\(\displaystyle\frac{{28}}{{53}}={1}-{2}{{\sin}^{{2}}\theta}\)

\(\displaystyle-\frac{{25}}{{53}}=-{2}{{\sin}^{{2}}\theta}\)

\(\displaystyle\frac{{25}}{{106}}={{\sin}^{{2}}\theta}\)

\(\displaystyle\sqrt{{\frac{{25}}{{106}}}}={\sin{\theta}}\)

\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\)

\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\times\frac{\sqrt{{106}}}{\sqrt{{106}}}\)

\(\displaystyle{\sin{\theta}}=\frac{{{5}\sqrt{{106}}}}{{106}}\)