如何使用pyspark中的dataframe中的两列对日期(两个日期之间)进行过滤

from pyspark.sql import SparkSession

spark = SparkSession.builder.getOrCreate()
df = spark.createDataFrame([
    ("2022-01-01", "2022-01-05", "data1"),
    ("2022-01-02", "2022-01-06", "data2"),
    ("2022-01-03", "2022-01-07", "data3"),
    ("2022-01-04", "2022-01-08", "data4")
], ["start_date", "end_date", "data"])

from pyspark.sql.functions import col, to_date

df = df.withColumn("start_date", to_date(col("start_date")))
df = df.withColumn("end_date", to_date(col("end_date")))

filtered_df = df.filter((col("start_date") >= "2022-01-02") & (col("start_date") <= "2022-01-04"))