Answer
$\dfrac{1}{2} [\cos ( \theta) +\cos (7 \theta) ] $
Work Step by Step
Recall the Product to Sum Identities:
$a) \sin x \cos y =\dfrac{1}{2} [\sin (x-y) +\sin (x+y)] \\ b) \sin x \sin y =\dfrac{1}{2} [\cos (x-y) -\cos (x+y)] \\ c) \cos x \cos y =\dfrac{1}{2} [\cos (x-y) +\cos (x+y)]$
We also know that $\cos$ and $\sec$ are even trigonometric functions.
This implies that $f (-x)=f(x) \implies \cos(-x)=\cos(x)$
By identity $(c)$, we have:
$\cos 3 \theta \ \cos 4 \theta=\dfrac{1}{2} [\cos (3 \theta- 4 \theta) +\cos (3 \theta+ 4 \theta) ] \\=\dfrac{1}{2} [\cos (- \theta) +\cos (7 \theta) ]\\=\dfrac{1}{2} [\cos ( \theta) +\cos (7 \theta) ] $
