MHB Solve for Theta: Equilibrium of a Particle

[Drain Brain]

solve for theta

$\frac{\tan(\theta)(\sqrt{5-4\cos(\theta)}-1)}{\sqrt{5-4\cos(\theta)}}=\frac{10}{60}$

I have already tried my best solving this eqn but still couldn't get it. FYI getting that equation already took me a lot of work. Now I'am on the last piece of the problem I am solving which is to solve for theta. So please kindly tell me how to go about it. Thanks! By the way the problem is about equlibrium of a particle. Thanks!

 

[phymat]

Well, you say that it took a lot of time for you to get this equation. So, I request you to cross check if the equation is correct.

 

[kaliprasad]

I think puttiing $\tan \theta = \dfrac{\sin \theta}{\cos \theta}$ shall comlpicate. I would square it and put $\tan^2\theta= \dfrac{ 1}{\cos ^2 \theta} -1$ then solve for $\cos \theta$

By the way could you mention what you have tried