Does Washington state law allow a landlord to invade my privacy for "inspection" several times a year when no problem exists?

We just rented a home, and the landlord wrote into the lease that he would enter for inspection 30 days after move-in, and then at "regular intervals" throughout the year. This seems a distinct intrusion into our privacy, and one we've never encountered in 30 years of renting! Even if he does give 48 hours notice, who wants an uninvited "guest" traipsing through their house every few weeks, spying on how they live? We have no pets, don't smoke, don't drink, don't do drugs, don't have parties - in other words, we're pretty much "model tenants" with sterling references. We'd rather not have our quiet lives interrupted regularly by a snoopy landlord - especially if the Landlord-Tenant Act gives us the expected right to privacy. Please help ASAP, as his first "inspection" is due soon.