Math Help - Trigonometric functions Factoring

1. Trigonometric functions Factoring

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

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

Now I'm stuck. The original equation is,

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

I need to factor the denominator so that I can apply the Trigonometric identity:
$sec^2{\theta} = 1+tan^2{\theta}$

2. $1 + 4\left(\frac{1}{2}\tan{\theta}\right)^2 =1 + 4\left(\frac{1}{4}\tan^2{\theta}\right)$

3. I feel like a ninny for missing that out.