Step 1:
The equations of the given planes are :
$7x+5y+6z+30=0$ and $3x-y-10z+4=0$
The direction cosines of $L_1$ are (7,5,6).
The direction cosines of $L_2$ are (3,-1,-10).
Step 2:
Therefore $\cos\theta=\begin{vmatrix}\large\frac{7\times 3+5\times -1+6\times -10}{\sqrt{7^2+5^2+6^2}\sqrt{3^2+(-1)^2+(-10)^2}}\end{vmatrix}$
$\Rightarrow \begin{vmatrix}\large\frac{21-5-60}{\sqrt{49+25+36}\sqrt{9+1+100}}\end{vmatrix}$
$\Rightarrow \large\frac{44}{\sqrt{49+25+36}\sqrt{9+1+100}}$
$\Rightarrow \large\frac{44}{\sqrt{110}\sqrt{110}}$
$\Rightarrow \large\frac{44}{110}$
$\Rightarrow \large\frac{2}{5}$
$\theta=\cos^{-1}\big(\large\frac{2}{5}\big)$