Answer
$\theta = 42.2^{\circ}$
Work Step by Step
$L = 6077-31~cos~2\theta$
$6074 = 6077-31~cos~2\theta$
$31~cos~2\theta = 6077-6074$
$cos~2\theta = \frac{3}{31}$
$2\theta = arccos(\frac{3}{31})$
$\theta = \frac{1}{2}~arccos(\frac{3}{31})$
$\theta = 42.2^{\circ}$
