1032: Solving the self-consistency equation of 1D step-index waveguide

Write a C program to solve the self-consistency equation:

 tan(pi * d / ld *sin(t))-sqrt(cos(tc)*cos(tc)/sin(t)/sin(t)-1) = 0

Find 't' in the region where 0 < pi * d / ld *sin(t) < pi / 2 and t < pi/2-tc

t should be in the unit of degree.

For example,

input: n1 n2 d ld

output: t

The output should round to three digits in the fraction part.

1.738 1.124 13.385 1.983 

4.000