计算：

(1) $\left[\left|8-6\right|-\left|4-7\right|\right]\times\frac{1}{\left|1-2\right|}$. (2) $a^{\frac{1}{2}}b^0\left(ab^2\right)^{-\frac{1}{2}}\div\left[b^{\frac{1}{3}}\left(a^3b^{-2}\right)^{-\frac{1}{3}}\right]$. (3) $\left(\lg50\right)^2+\lg2\cdot\lg\left(50^2\right)+\left(\lg2\right)^2$. (4) $\sin105^\circ+\sin15^\circ$. (5) $\displaystyle\lim_{n\to\infty}\frac{5-2n+3n^2}{4n^2-n-7}$. (6) $\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}+\sqrt{\frac{1+\cos\theta}{1-\cos\theta}}$.