The value of $({\cos }^{4}1°+{\cos }^{4}2°+{\cos }^{4}3°+\mathrm{....}+{\cos }^{4}179°)-({\sin }^{4}1°+{\sin }^{4}2°+{\sin }^{4}3°+\mathrm{....}+{\sin }^{4}179°)=\_\_\_$ 

 ${\cos }^4\theta -{\sin }^4\theta =({\cos }^2\theta +{\sin }^2\theta )({\cos }^2\theta -{\sin }^2\theta )=1\times \cos 2\theta$
 $\Rightarrow \cos 2+\cos 4+\cos 6+\mathrm{.....}+\cos 358$
 $\Rightarrow 2(\cos 2+\cos 4+\mathrm{.....}+\cos 178)+\cos 180$
 $n=89,\alpha =2,\beta =2$
 $\Rightarrow 2\frac{\sin 89}{\sin 1°}\cos 90°+(-1)=-1$