2015 AMC 12A Question 24

Rational numbers $a$ and $b$ are chosen at random among all rational numbers in the interval $[0, 2)$ that can be written as fractions $\dfrac{n}{d}$ where $n$ and $d$ are integers with $1 \le d \le 5.$ What is the probability that $$
(\cos(a\pi) + i\sin(b\pi))^4
$$ is a real number?