Consider the following for the next items that follow:

Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$.

What is pq equal to ?

Consider the following for the next items that follow:

Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$.

For how many values of x does $\frac{1}{p}$ become zero?

Consider the following for the next items that follow:

Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$

What is a value of sin 3x + sin 3y?

Consider the following for the next items that follow:

Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$

What is a value of cos³ x + cos³ y?