2 In A Row

You have a coin where you can decide the probability $p$ of obtaining a heads before flipping the coin $4$ times. What value of $p$ maximizes the probability that you obtain exactly two consecutive heads in your $4$ flips? For example, $HHHT$ and $HHHH$ are not allowed, but $HHTH$ is allowed. The answer is in the form $\dfrac{a-\sqrt{b}}{c}$ for integers $a,b,$ and $c$ with $c$ minimal. Find $a + b + c$.