Introducción al área acotada por curvas polares

Sea $R$R la región delimitada por la curva polar $r(\theta)=2-2\cos(\theta)$r, left parenthesis, theta, right parenthesis, equals, 2, minus, 2, cosine, left parenthesis, theta, right parenthesis, donde $\dfrac{2\pi}{3}\leq \theta\leq \pi$start fraction, 2, pi, divided by, 3, end fraction, is less than or equal to, theta, is less than or equal to, pi.