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So, I need to invert the following function

enter image description here and express alpha 2 in terms of D, where both t and alpha 1 are constant. Someone suggested the Newton-Raphson method, and here's what I've done so far

enter image description here enter image description here

Okay, but what do I do now? Any help would be appreciated. Sorry for the bad formatting.

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    may be that a judicious choice of trigonometric substitution could help here? Thinking something like $\sec{x} = \sqrt{\tan^2{x} + 1}$ – 2017-02-23
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    It seems to me that the Newton-Raphson method would only be useful if you have numerical values for the other parameters. The method is not going to give you a solution of $\alpha_2$ expressed in terms of other variables, but only a numerical value given values for the other parameters and an accuracy bound. – 2017-02-23

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