\(A = {\sin ^2}{15^0} + {\sin ^2}{25^0} + {\sin ^2}{35^0} + {\sin ^2}{45^0} + {\sin ^2}{55^0} + {\sin ^2}{65^0} + {\sin ^2}{75^0}\) 

\(\,\,A = {\sin ^2}{15^0} + {\sin ^2}{25^0} + {\sin ^2}{35^0} + {\sin ^2}{45^0} + {\sin ^2}55 + {\sin ^2}{65^0} + {\sin ^2}{75^0}\) 

Ta có:

\(\begin{array}{l}A = {\sin ^2}{15^0} + {\sin ^2}{25^0} + {\sin ^2}{35^0} + {\sin ^2}{45^0} + {\sin ^2}55 + {\sin ^2}{65^0} + {\sin ^2}{75^0}\\\,\,\,\,\, = {\sin ^2}{15^0} + {\sin ^2}{25^0} + {\sin ^2}{35^0} + {\sin ^2}{45^0} + {\cos ^2}{35^0} + {\cos ^2}{25^0} + {\cos ^2}{15^0}\\\,\,\,\,\, = \left( {{{\sin }^2}{{15}^0} + {{\cos }^2}{{15}^0}} \right) + \left( {{{\sin }^2}{{25}^0} + {{\cos }^2}25} \right) + \left( {{{\sin }^2}{{35}^0} + {{\cos }^2}{{35}^0}} \right) + {\sin ^2}{45^0}\\\,\,\,\, = 1 + 1 + 1 + {\left( {\dfrac{{\sqrt 2 }}{2}} \right)^2} = 3 + \dfrac{1}{2} = \dfrac{7}{2}.\end{array}\)