how to solve complex optimization problem?

Question

I have bunch of equations of the form $$R = V(1) \cdot \cos(\theta) + V(2) \cdot \sin(\theta)$$ with known R and $\theta$ (with measurement errors). With ordinary least squares method, I estimated angle and magnitude of vector $V$. Magnitude of estimated vector seems reasonable where as the angle seem to vary a lot. Hence I tried using orthogonal regression to correct the effects of measurement errors on $R$ and $\theta$. The orthogonal regression estimator is then obtained by minimizing, $$\sum_{i=1}^{N} (R_{i} - V(1) \cdot \cos(\alpha_{i}) - V(2) \cdot \sin(\alpha_{i}))^{2} + \eta (\theta_{i} - \alpha_{i})^{2}$$ where $\alpha$ are the true values of $\theta$ and $\eta$ is ratio of error-variance of R and $\theta$. But this a large complex optimization problem with not only two unknown components of vector V but also $\alpha$ (true values of $\theta$). Hence, I am finding it difficult to solve this optimization problem. Please suggest me a method to solve the equation.