I tried to factor $\displaystyle 1+4(\frac{1}{2}tan^2{\theta})$ to be equal to $\displaystyle 1+tan^2{\theta}$ but I'm having a hard time. Any tips to start me out?

I tried to factor out 2 making it $\displaystyle 2(\frac{1}{2}+tan^2{\theta})$

Now I'm stuck. The original equation is,

$\displaystyle \int{\frac{1}{1 + 4\left(\frac{1}{2}\tan{\theta}\right)^2}\left(\fra c{1}{2}\sec^2{\theta}\right)\,d\theta}$

I need to factor the denominator so that I can apply the Trigonometric identity:

$\displaystyle sec^2{\theta} = 1+tan^2{\theta}$