Exploring the sensitivity of current and future experiments to $θ_{\odot}$

The first results from the KamLAND experiment in conjunction with the global solar neutrino data has demonstrated striking ability to constrain the $\Delta m^2_\odot$ ($\Delta m^2_{21}$) very precisely. However the allowed range of $\theta_{\odot}$ ($\theta_{12}$) did not change much with the inclusion of the KamLAND results. In this paper we probe if future data from KamLAND can increase the accuracy of the allowed range in $\theta_{\odot}$ and conclude that even after 3 kton-year of statistics, KamLAND may find it hard to improve the bounds on the mixing angle obtained from the current solar neutrino data. We discuss the $\theta_{12}$ sensitivity of the survival probabilities in matter (vacuum) as is relevant for the solar (KamLAND) experiments. We find that the presence of matter effects in the survival probabilities for $^8B$ neutrinos give the solar neutrino experiments SK and SNO an edge over KamLAND, as far as $\theta_{12}$ sensitivity is concerned, particularly near maximal mixing. Among solar neutrino experiments we identify SNO as the most promising candidate for constraining $\theta_{12}$ and make a projected sensitivity test for the mixing angle by reducing the error in the neutral current measurement at SNO. Finally we argue that the most accurate bounds on $\theta_{12}$ can be achieved in a reactor experiment, if the corresponding baseline and energy can be tuned to a minimum in the survival probability. We propose a new reactor experiment which can give the value of $\tan^2\theta_{12}$ to within 14%. We also discuss the future Borexino and LowNu experiments.