I can't seem to do (a)(ii) of this question, there are probably two ways to do it but i get stuck using my way.

Given $\displaystyle 4cos\theta+3sin\theta=Rcos(\theta-\alpha)$ find the value of E and the value of $\displaystyle \alpha$ where R>0 and 0<$\displaystyle \alpha<\frac{\pi}{2}$

[I got R = 5 and [tex]\alpha=0.6435 rads which is right]

Hence ind all values between 0 and 2$\displaystyle \pi$ satisfying

(a)(i) 4cos$\displaystyle \theta+3sin\theta=2$

[i also got this right its 1.8 and 5.77 rads]

(ii) 4cos$\displaystyle 2\theta+3sin2\theta=5cos\theta$

i expanded again and got 5cos($\displaystyle (2\theta-0.64350)=5cos\theta$ but i dont know where to go from here,,,ive come across a similar scenario before and cant remember what I did, If anybody could help that'd be great, thnx