Trigo + Binomial!

Discrete Mathematics Level 4

\[ 1+\dfrac{1}{3}+\dfrac{1}{3}\cdot\dfrac{3}{6}+\dfrac{1}{3}\cdot\dfrac{3}{6}\cdot\dfrac{5}{9}+\dfrac{1}{3}\cdot\dfrac{3}{6}\cdot\dfrac{5}{9}\cdot\dfrac{7}{12}+\cdots=2\cos\theta\]

Find the value of \(\theta\) in degrees if \(0 \le \theta \le π\) .