`4\ tan x− sec^2x= 0`

Writing this in terms of `sin x` and `cos x` only:

`4(sin x)/(cos x)-1/(cos^2x)=0`

Multiplying throughout by `cos x`:

`4\ sin x\ cos x=1`

Dividing both sides by 2:

`2\ sin x\ cos x=1/2`

Recognizing the LHS is `sin 2x`, from before:

`sin 2x,=0.5`

In 0 ≤ x < 2π, we need to find values of 2x such that 0 ≤ 2x < 4π. (Twice the original domain.)

So the values for `2x` are:

`2x=pi/6,(5pi)/6,(13pi)/6,(17pi)/6`

Dividing throughout by 2 gives our required values for `x`:

`x=pi/12,(5pi)/12,(13pi)/12,(17pi)/12`

or, in decimal form:

`x = 0.2618, 1.309, 3.403, 4.451`