Can you help me find the residues of $\int _{0}^{2\pi}\frac{cos3\theta} {5-4cos \theta}d\theta = \frac{\pi}{12}$

The intergrand has a pole of order 3 at z=0 and a simple pole z=1/2 inside C but I don’t know how to find their residues. Can somebody help me pls?

More details: convert from polar to z ∫2π0cos3θ/5−4cosθdθ=−1/2i∮Cz6+1(z3)(2z−1)(z−2)dz