Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.
4 sin²(<em>θ</em>) - 1 = 0
==> sin²(<em>θ</em>) = 1/4
==> sin(<em>θ</em>) = ±1/√2
==> <em>θ</em> = <em>π</em>/4, 3<em>π</em>/4, 5<em>π</em>/4, 7<em>π</em>/4
