Question 6
Find the largest possible value of
$$
\left(\sin \theta_{1}\right)\left(\cos \theta_{2}\right)+\left(\sin \theta_{2}\right)\left(\cos \theta_{3}\right)+\cdots+\left(\sin \theta_{2013}\right)\left(\cos \theta_{2014}\right)+\left(\sin \theta_{2014}\right)\left(\cos \theta_{1}\right)
$$
$$
\left(\sin \theta_{1}\right)\left(\cos \theta_{2}\right)+\left(\sin \theta_{2}\right)\left(\cos \theta_{3}\right)+\cdots+\left(\sin \theta_{2013}\right)\left(\cos \theta_{2014}\right)+\left(\sin \theta_{2014}\right)\left(\cos \theta_{1}\right)
$$