you can rearrange gif.latex.gifand gif.latex.gif to simplify the inside the integrals to get

gif.latex.gif

use substitution gif.latex.gif

then gif.latex.gif

gif.latex.gif

gif.latex.gif

let gif.latex.gif

gif.latex.gif constant

From the you can see the integrals is tan inverse of \sqrt{u^2-1}

We can back track to find it in terms of theta

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