China Mathematical Competition (Hainan)

Let $\theta$ be an acute angle such that the equation $x^2+4x\cos \theta +c\cot \theta =0$ involving variable $x$ has multiple roots. Then the measure of $\theta$ in radians is ( ). (A) $\frac{\pi }{6}$ (B) $\frac{\pi }{12}$ or $\frac{5\pi }{12}$ (C) $\frac{\pi }{6}$ or $\frac{5\pi }{12}$ (D) $\frac{\pi }{12}$