Find the combined equation of the lines through the origin :
(1) each making an ange of `45^(@)` with the line `3x + y = 2.`
(2) each making an angle of `pi//6` with the line `3x + y - 6 = 0` .
(3) which form an equilateral triangle with the line `3x + 4y = 8.`

Explanation

To solve the problem of finding the combined equations of lines through the origin for the given conditions, we will break it down into three parts as specified in the question.

### Part 1: Lines making an angle of 45 degrees with the line \(3x + y = 2\)

1. **Find the slope of the given line:**
The equation of the line is \(3x + y = 2\). Rearranging it to slope-intercept form:
\[
y = -3x + 2
...