\(\sqrt{3}\sin\theta+\cos\theta\) \(=2\sin\left(\theta+\dfrac{\pi}{6}\right)\)
\(\sin\theta+\cos\theta\) \(=\sqrt{2}\sin\left(\theta+\dfrac{\pi}{4}\right)\)
\(\sin\theta+\sqrt{3}\cos\theta\) \(=2\sin\left(\theta+\dfrac{\pi}{3}\right)\)

\(\sqrt{3}\sin\theta-\cos\theta\) \(=2\sin\left(\theta-\dfrac{\pi}{6}\right)\)
\(\sin\theta-\cos\theta\) \(=\sqrt{2}\sin\left(\theta-\dfrac{\pi}{4}\right)\)
\(\sin\theta-\sqrt{3}\cos\theta\) \(=2\sin\left(\theta-\dfrac{\pi}{3}\right)\)

\(\sqrt{3}\sin\theta+\cos\theta\) \(=2\cos\left(\theta-\dfrac{\pi}{3}\right)\)
\(\sin\theta+\cos\theta\) \(=\sqrt{2}\cos\left(\theta-\dfrac{\pi}{4}\right)\)
\(\sin\theta+\sqrt{3}\cos\theta\) \(=2\cos\left(\theta-\dfrac{\pi}{6}\right)\)

\(\sqrt{3}\sin\theta-\cos\theta\) \(=2\cos\left(\theta-\dfrac{2}{3}\pi\right)\)
\(\sin\theta-\cos\theta\) \(=\sqrt{2}\cos\left(\theta-\dfrac{3}{4}\pi\right)\)
\(\sin\theta-\sqrt{3}\cos\theta\) \(=2\cos\left(\theta-\dfrac{5}{6}\pi\right)\)