Cosmology Problem, Friedman equation

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The discussion focuses on solving the Friedman equation for a universe with negative curvature (k<0) by substituting the scale factor \( a = b(1 - \cos(\theta)) \) and time \( t = c(\theta - \sin(\theta)) \). Participants are seeking guidance on the general procedure for solving this equation, particularly in relation to the application of the chain rule for derivatives. The challenge lies in eliminating cosine terms during the differentiation process, which is crucial for simplifying the equation.

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I am asked in a question to show that the friedman with k<0 equation can be solved by substituing

a= b(1-cos(theta)) and t = c(theta- sin(theta).

a is scale factor,
t is time
b,c are constants

Can anyone outline the general procedure to go about solving this.

I've tried substituting da/dt using the chain rule to obtain da/d(theta)*d(theta)/dt, but this leads to an uneliminated cos terms...
 
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Can you please write the friedman equation. Need to know your notations.
 

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