Understand and use the exact values of cos(𝜃), sin(𝜃) and tan(𝜃) at integer multiples of π 6 and π 4.

Determine the exact value of the following expression. $$\cos\left(\frac{5\pi}{6}\right) + 2\sin\left(\frac{\pi}{4}\right) - \tan\left(\frac{\pi}{3}\right)$$

Evaluate $\cos\left(\frac{5\pi}{6}\right) + \sin\left(\frac{7\pi}{4}\right)$.

Determine all values of \(x\) that satisfy \(\sqrt{3}\tan(x) + 1 = 0\), where \(0 \leq x \leq 2\pi\). Express your answers in exact form using radians.