Write SQL query to solve given problem: Calculate the total amount paid by Stephanie Mitchell for film rentals in June 2005.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT SUM(T1.amount) FROM payment AS T1 INNER JOIN customer AS T2 ON T1.customer_id = T2.customer_id WHERE T2.first_name = 'STEPHANIE' AND T2.last_name = 'MITCHELL' AND SUBSTR(T1.payment_date, 1, 7) = '2005-06'