At the interface between two materials having refractive indices \( n_1 \) and \( n_2 \), the critical angle for reflection of an EM wave is \( \theta_c \). The \( n_1 \) material is replaced by another material having refractive index \( n_3 \), such that the critical angle at the interface between \( n_1 \) and \( n_3 \) materials is \( \theta_{c3} \). If \( n_1>n_2>n_3 \), \( \frac{n_2}{n_3} = \frac{2}{5} \), and \( \sin\theta_{c2} - \sin\theta_{c1} = \frac{1}{2} \), then \( \theta_{c1} \) is: