If \( \int \frac{\cos x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}} d x=f(x)\left(1+\sin ^{6} x\right)^{\frac{1}{\la…

If \( \int \frac{\cos x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}} d x=f(x)\left(1+\sin ^{6} x\right)^{\frac{1}{\lambda}}+c \), where \( c \) is a constant of integration, then \( \lambda \mathrm{f}\left(\frac{\pi}{3}\right) \) is equal to

[JEE Main 2020, 8 Jan (Shift 1)]