Inserting multiple rows wtih a SELECt in the values clause

OK, now that figured out how to return the constant, this is the final
query I need to run.

INSERT into rate
(
employee_key ,
project_key ,
work_type_key ,
rate
)
VALUES
(
(
SELECT
employee.employee_key ,
project.project_key ,
work_type.work_type_key ,
1 as rate
FROM employee
CROSS JOIN project
CROSS JOIN work_type
)
);

But this fails.

I suspect this may be because the SELECT in the values clause returns
multiple rows?

--
"They that would give up essential liberty for temporary safety deserve
neither liberty nor safety."
-- Benjamin Franklin