Figure 2 shows part of the curve with equation y = (2x - 1) tan 2x, 0 < x < π/4 The curve has a minimum at the point P - Edexcel - A-Level Maths Pure - Question 7 - 2006 - Paper 4

Using the iterative formula:

1. Calculate x_1:
   $x_1 = \frac{1}{2} (2 - \sin 4 \times 0.3)$

Performing this calculation yields:
$x_1 = 0.2670$
2. Now, calculate x_2:
$x_2 = \frac{1}{2} (2 - \sin 4 \times 0.2670)$

This gives:
$x_2 = 0.2809$
3. Next, for x_3:
$x_3 = \frac{1}{2} (2 - \sin 4 \times 0.2809)$

Resulting in:
$x_3 = 0.2746$
4. Finally, calculate x_4:
$x_4 = \frac{1}{2} (2 - \sin 4 \times 0.2746)$

This yields:
$x_4 = 0.2774$

To finalize, we observe that through continuous iterations, we can approximate k as follows:
Given that x_4 = 0.2774, rounding to three significant figures gives k = 0.277.
Thus, we conclude that k approximates to 0.277.