The value of $\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ}=$

If $\mathrm{f}(x)=\cos (\log x)$ then $\mathrm{f}\left(x^2\right) \cdot \mathrm{f}\left(y^2\right)-\frac{1}{2}\left[\mathrm{f}\left(\frac{x^2}{y^2}\right)+\mathrm{f}\left(x^2 y^2\right)\right]$ has the value

$$ 3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}= $$

The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ}=0.0175^{\mathrm{c}}, \sin 60^{\circ}=0.8660$ )