Indefinite Integrals

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