I need to calculate two coefficients: k and n. This involves solving two equations for k and n:
$$\frac{(8 \pi d)}{\lambda }{kn}=\frac{\text{$\triangle $I}}{I}$$
$$\text{$\triangle $l}_2=\left\{\frac{\lambda }{2 \pi }\right\} \tan ^{-1}\left(\frac{2 \left(n \sin \left(\frac{4 \pi d n}{\lambda }\right)+k\right)}{\frac{4 \pi d \left(n^2-1\right)}{\lambda }+\left(n^2+1\right) \cos \left(\frac{4 \pi d n}{\lambda }\right)}\right)$$
I have all coefficients, except for k and n. Roughly:
$$k n=0.00730621$$
$$\tan ^{-1}\left(\frac{2 (k+n \sin (8.89655 n))}{8.89655 \left(n^2-1\right)+\left(n^2+1\right) \cos (8.89655 n)}\right) = 309.526$$ How should I tackle it?
I tried to solve this on Mathematica, but neither Solve, nor NSolve could manage it.
Thanks.