\(\mathrm{a}=\mathrm{A} \sin \omega \mathrm{t}_{0}\)

\(b=A \sin 2 \omega t_{0}\)

\(c=A \sin 3 \omega t_{0}\)

\(\mathrm{a}+\mathrm{c}=\mathrm{A}\left[\sin \omega \mathrm{t}_{0}+\sin 3 \omega t_{0}\right]\)\(=2 \mathrm{A} \sin 2 \omega \mathrm{t}_{0}\cos \omega t_{0}\)

\(\frac{a+c}{b}=2 \cos \omega t_{0}\)

\(\Rightarrow \omega=\frac{1}{t_{0}} \cdot \cos ^{-1}\left(\frac{a+c}{2 b}\right)\)

\( \Rightarrow f=\frac{1}{2 \pi t_{0}} \cos ^{-1}\left(\frac{a+c}{2 b}\right)\)