Solving a set of 3 Nonlinear Equations

In the following 3 equations:

${k}_{1}{\mathrm{cos}}^{2}(\theta )+{k}_{2}{\mathrm{sin}}^{2}(\theta )={c}_{1}$

$2({k}_{2}-{k}_{1})\mathrm{cos}(\theta )\mathrm{sin}(\theta )={c}_{2}$

${k}_{1}{\mathrm{sin}}^{2}(\theta )+{k}_{2}{\mathrm{cos}}^{2}(\theta )={c}_{3}$

${c}_{1}$, ${c}_{2}$ and ${c}_{3}$ are given, and ${k}_{1}$, ${k}_{2}$ and $\theta $ are the unknowns. What is the best way to solve for the unknowns?

In the following 3 equations:

${k}_{1}{\mathrm{cos}}^{2}(\theta )+{k}_{2}{\mathrm{sin}}^{2}(\theta )={c}_{1}$

$2({k}_{2}-{k}_{1})\mathrm{cos}(\theta )\mathrm{sin}(\theta )={c}_{2}$

${k}_{1}{\mathrm{sin}}^{2}(\theta )+{k}_{2}{\mathrm{cos}}^{2}(\theta )={c}_{3}$

${c}_{1}$, ${c}_{2}$ and ${c}_{3}$ are given, and ${k}_{1}$, ${k}_{2}$ and $\theta $ are the unknowns. What is the best way to solve for the unknowns?