# Can't solve this equation to $\phi$

It's the end of a Physics Problem. 2 Forces are equal, one is proportional to $\sin\phi$ the other to $$\frac{\cos\phi}{\text{distance}^2}$$ distance is proportional to $\sin\phi$  I'm stuck at this last equation $$\frac{\sin^3\phi}{\cos\phi}=c$$

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I solved it to $$\phi=\arcsin x$$ $$\frac{x^3}{\sqrt{1-x^2}}=c$$ $$\frac{x^6}{1-x^2}=c^2$$ But I think one can only solve this numerical