Paginate wp_query while utilizing post__not_in

I’m currently running a wp_query like this:

<?php 
            $the_query = new WP_Query( array(
                'post_type' => 'photos',
                'posts_per_page' => '2',
                'post__not_in' => array(3),
                'paged' => $paged
                )
            );
        ?>
        <?php while ( $the_query->have_posts() ) : $the_query->the_post(); ?> 
         <?php the_title(); ?>
        <?php endwhile; ?>

I then have some pagination at the bottom as such:

<?php next_posts_link(); ?>
<?php previous_posts_link(); ?>

Say I have 11 posts that the query would return but one of them has the id of ‘3’. This means that I have 10 total posts and should return a number of ‘next’ links. For whatever reason at the end of those pages, there will be a ‘next’ link that links to a page that is blank.

I believe this empty page is the post I’m attempting to exclude with ‘post__not_in’.

How can I exclude posts from my wp_query and still have accurate pagination?