Trigonometric Ratios & Id question bank (Maths)

The value of $\left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right)$ is

Let $|\cos \theta \cos (60-\theta) \cos (60+\theta)| \leq \frac{1}{8}, \theta \epsilon[0,2 \pi]$. Then, the sum of all $\theta \epsilon[0,2 \pi]$, where $\cos 3 \theta$ attains its maximum value, is :