Let $\widehat a$ and $\widehat b$ be two unit vectors such that $|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2$. If $\theta$ $\in$ (0, $\pi$) is the angle between $\widehat a$ and $\widehat b$, then among the statements :

(S1) : $2|\widehat a \times \widehat b| = |\widehat a - \widehat b|$

(S2) : The projection of $\widehat a$ on ($\widehat a$ + $\widehat b$) is ${1 \over 2}$